http://en.wikipedia.org/wiki/List_of_largest_airlines

It list airlines by:

World

• 1.1 Scheduled passengers carried of the IATA members
• 1.2 Scheduled international passengers carried of the IATA members
• 1.3 Total scheduled passenger-kilometers flown in 2005 of the IATA members [21]
• 1.4 Total scheduled freight tonne-kilometers flown in 2005 of the IATA members[22]
• 1.5 By fleet size in 2006

Lufthanza has the second largest fleet size and is the largest carrier of international passangers.