He initially flew two seaters but later joined Jasta 34b flying fighters and by the spring of 1918 he had over a dozen victories to his name.
He flew Dr.1. 521/17 for a period in 1918, after Jasta 34b had been equipped with 'cast-off's from Jagdgeschwader (I). Even though the machines were second hand, they were warmly welcomed by Jasta 34b as being superior to the older Albatros and Pfalz fighters they had been previously equipped with.
In June 1918 Greim had an encounter with a Bristol Fighter, and his aircraft lost its cowling. This struck and damaged his top wing, along with the lower left interplane strut, but he managed to land the machine successfully.
By the war's end he had scored 28 victories, and had been awarded the Pour le Mérite, and the Bavarian Max-Joseph Order. This latter award made him a Knight (Ritter), and allowed him to add the title 'von' to his name.
Greim rose to the rank of General Feldmarscall in the Luftwaffe during the Second World War but committed suicide in May 1945, following Germany's defeat. He was at the time, the acting commander of the Luftwaffe.