Prices edged up by 0.4% month-on-month in May to reach £167,912 on average, the building society said. House prices are now 1.1% higher than they were a year ago - marking the fastest annual increase seen since November 2011.
The study is the latest in a string of reports which have pointed to returning confidence in the housing market in 2013 as borrowers find it easier to access a mortgage.
The number of mortgages on the market has increased sharply since the Government launched a scheme called Funding for Lending last August, which has given lenders access to cheap finance to help borrowers.
Lenders have been slashing their rates and they have also reported increased numbers of first-time buyers entering the market. Government schemes called NewBuy and Help to Buy have also been introduced to specifically give people with smaller deposits a helping hand.
Robert Gardner, Nationwide's chief economist, said: "A number of factors are likely to be contributing to the pick up in activity.
"With the UK returning to growth in the first quarter of 2013, the improvement in wider economic conditions may also be playing a role in boosting sentiment."
Mr Gardner said the ongoing low interest rates combined with Government policy provided reasons for "optimism" that activity would continue to gather pace in the coming months. But he cautioned that progress was likely to be gradual, with a continued tough jobs market and pressure on household budgets.
"In real terms, average weekly wages have been falling for some time and are now back at the level prevailing in late 2003," he said.