Europe's biggest low-cost airline transported 5.5 million passengers over the course of the month, which represents a nine percent increase from the same month last year.
In contrast, British Airways carried 1.7 million passengers, which is a decline of eight percent from May 2008.
Ryanair's head of communications Stephen McNamara said that the carrier was seeing its passenger traffic "grow each month".
"Ryanair now carries three times the monthly traffic of BA in the UK and Europe and we will continue to grow as even more passengers become price sensitive and Ryanair continues to [deliver] lower fares," he commented.
The airline recently introduced online check-in only, and hopes to phase out the use of airport check-in desks completely by October 1st.
Ryanair currently operates 830 routes from its 32 bases, with its largest being Dublin Airport and Stansted Airport.
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