Ryanair says it carried 7.15 million passengers last month, an increase of 11% on May last year.
The load factor, or percentage of seats filled, edged up one point from a year earlier to 82%.
Last month, Ryanair chief Michael O'Leary said its traffic numbers were expected to grow by 10% in the six months to the end of September, falling by 4% in the nex six months.
At the release of the company's annual results, he said he remained concerned at the impact of the recession, austerity measures and falling consumer confidence on fares.
