The group, which represents carriers including Easyjet, Ryanair and British Airways' parent company IAG, claimed some passengers are missing their flights because of the issue.
New European Union rules introduced following terror attacks in Paris and Brussels require countries to carry out more stringent checks on travellers entering and leaving the Schengen area, which allows passport-free movement across much of the EU.
The change means the details of passengers from non-Schengen countries, such as the UK, are run through databases to alert authorities if they are known to pose a threat.
A4E managing director Thomas Reynaert said: "Travellers face long lines and can't get on their flights. Queuing for up to four hours has been the top record these days.
"Airports like Madrid, Palma de Mallorca, Lisbon, Lyon, Paris-Orly, Milan or Brussels are producing shameful pictures of devastated passengers in front of immigration booths, in lines stretching hundreds of metres.
"At some airports, flight delays have increased by 300% compared to last year."
A4E warned that the situation could worsen in the coming weeks as the new regulations have not yet been fully implemented. The six-month period to put the enhanced checks in place ends on October 7.
Mr Reynaert urged the countries affected to "deploy appropriate staff and resources" to carry out the checks.
"Member states need to take all necessary measures now to prevent such disruptions," he added.
A spokeswoman for travel trade organisation Abta said: "New, stricter passport checks are resulting in longer queues at some airports, including Palma, which is already busy due to a significant increase in passenger numbers.
"Tour operators will ensure that customers get to the airport in plenty of time so that they are not in danger of missing their flights.
"However, independent travellers will need to check the situation with their airlines and, where necessary, ensure they factor these longer queuing times into their travel plans when flying in and out of the airport.
"It is also extremely important that border control check points are sufficiently resourced so that queuing times are kept to a minimum."
Airport security gone mad?
Airport security gone mad?
Last March, a toddler in a wheelchair was subjected to an invasive body search and swabbed for explosives on his way to Disneyland. His father, who filmed the incident, which took place at Chicago O'Hare Airport, said: "He was trembling with fear... I was told I could not touch him or come near him during this process."
A man who is believed to posess "the world's largest penis" sparked a security scare after airport staff at San Francisco International Airport thought he might have been concealing a weapon. Jonah Falcon (pictured) was subjected to a rigorous patdown and had powder sprinkled on his pants to check for explosives...
Last Christmas, an 85-year-old woman in a wheelchair claimed she was strip-searched at JFK Airport, New York. Leonore Zimmerman, who has a defibrillator for heart problems, was worried that the scanners would interfere with her life-saving device, so asked for a pat down. Instead, she says she was taken to a private room and told to remove her clothes in a humiliating search that also left injured. The process took so long that she also missed her flight. Howver, the TSA denied the incident had taken place.
In June, a passenger was left devastaed after a TSA official spilled the ashes of his grandfather over the terminal floor. John Gross was attempting to take the ashes home to Indianapolis when he was stopped at security. He claims she dipped her finger into the jar, spilling its contents onto the floor, despite TSA rules that state that a crematory container are to be opened in no circumstances.
This summer, a report revealed that a disproportionate amount of women were being singled out for strip searches at Gatwick Airport. The government's chief investigator of immigration John Vine, also revealed that Afro-Caribbean women in particular were being targeted. Reasons given for strip searches by Border Force staff at Gatwicks' North Terminal included only buying a ticket one day before travel, they were carrying £200 in cash, and because they were visiting the UK to look for hair and beauty products. New guidance on searches has since been rewritten.
One US passenger Mandi Hamlin hit the press a couple of years ago when she was stopped and wanded by a TSA employee and asked to remove her metal nipple rings. One came out with no problem, but the other got stuck - and eventually had to be removed using pliers. OUCH.
Last year, security officials at Gatwick Airport banned a passenger from carrying a toy soldier on a transatlantic flight. The three-inch plastic toy gun was branded a 'firearm'. Passenger Julie Lloyd, who had bought the figure as a present for her husband, told the Daily Mail:"It is only three inches long and there are no moving parts. There isn't even a trigger." She eventually posted it to herself instead.
When two children tried to take their Christmas gift of Play-Doh past the checkpoint at New Orleans airport, an overzealous agent confiscated it, despite the fact Play-Doh is not on the list of prohibited items. Apparently, aents can use "their own discretion". Never mind that millions have been invested on explosive detection equipment: it wasn't deemed necesary to use it. Running Play-Doh through the explosives detector would have taken under a minute...
In 2011, security officials at Florida airport patted down a 95-year-old cancer sufferer and made her remove her adult 'nappy' during the search. She was then forced to go through airport security without any underwear. CNN reported that Jena Weber was travelling with her mother, who was in the final stages of her battle with leukaemia, last June to see relatives. In response to the incident, the TSA said:"We have reviewed the circumstances involving this screening and determined that our officers acted professionally and according to proper procedure."
... meanwhile, in August 2012, a boy of 11 managed to slip through security at Manchester Airport and fly to Rome without a passport or barding pass. Liam Corcoran evaded five security checks to join the Jet2.com flight unaccompanied.
2012 was the year of "naked" body scanner in the UK - and it caused massive controversy. Passengers refusing to pass through them have, in the past, been banned from flying. The scanners -0 which gave security officers an eyeful - have now been banned by the EU, (ironically on safety grounds) - but not before millions have been spent on installing them... plane madness? We think so!