Ryanair saw passenger numbers rise by 5% or 350,000 to 7.86 million in May over the same month last year.
Overall carryings for the 12 months to May were up by 4% to a record 79.8 million.
A spokesman said: “Ryanair’s traffic increased by 5% over May 2012 and our load factor rose by 1%, as we enjoyed a record 12-month period with almost 80 million passengers choosing one of our ultra-low fares since May 2012, a rise of 4%.”