Lufthansa carried 9.23 million passengers in May, 0.3% more than in the same month last year.
Taking the five months to May as a whole, passenger numbers grew 3.6% to 39.83 million, Lufthansa said in a statement.
The key seat-load factor, which measures the number of seats filled on flights, slipped 0.1% to 77.9% in May alone, but increased by 1.1% to 75.9% over the five-month period.
In the wake of the global economic slowdown, the cargo division, Lufthansa Cargo, saw the freight fall 12.3% to 144,000 tonnes in May alone and by 10.2% to 713,000 tonnes in the January-May period.