The Dublin-based carrier said bookings from passengers in the UK, Germany and Scandinavia were particularly robust as revenues rose 15% to 969 million euro (£825 million) in the three months to December 31.
Low-cost airline Ryanair gave another boost to its profits guidance after benefiting from strong demand for pre-Christmas flights.
It now expects profits of around 540 million euro (£460 million) in the year to March, which would represent a 7% increase on last year's performance despite a 19% rise in oil costs.
Ryanair also increased its full-year profits guidance in November to between 490 million and 520 million euro (£417 million-£442 million), up from 400 million to 440 million euro previously forecast.
Quarterly passenger numbers increased by 3% to 17.3 million, while an 8% rise in average fares meant third quarter profits were up 21% to 18.1 million euro (£15.4 million) in the period.
The airline has grounded up to 80 aircraft this winter as a result of high oil prices, airport fees at Stansted and Dublin airports and expectations for seasonally weaker demand. As a result, it expects traffic will be 3% lower in the current quarter, which is equivalent to around 400,000 passengers.
Ryanair opened its 51st base in Maastricht in December and will open six more from April in Eindhoven, Krakow, Zadar in Croatia, Chania in Greece and Marrakesh and Fez in Morocco.
It said significant capacity cuts by other carriers would also offer it growth opportunities across Europe. The company added: "We expect further capacity cuts and restructurings in Europe as high fare, loss making carriers struggle to compete with Ryanair's expansion at low prices."
Despite the tough market conditions, analysts at Panmure Gordon stockbrokers said the cuts in capacity growth and higher competitor fares should translate into "attractive and sustainable" profits growth for Ryanair.
Analyst Gert Zonneveld described the third quarter performance as excellent and said Panmure continued to hold a buy recommendation on Ryanair.