Greim served the German Empire in World War 1. He was in the artillery until 1915, when he transferred to the German Air Service. He served as a artillery spotter observer on a FFA 3b when he got his first aerial victory on October 15, 1915. He then served on a FFA 204 while fighting at the Somme. In 1917 he finished pilot training and joined a FA 46b. Soon he became an ace with 7 victories. He kept getting more and more victories. In June 1918 Greim was almost shot down by a British Bristol F.2 Fighter but managed to land the plane. On August 23, he and Johan Putz in one of the first ever assaults on tanks by aircraft. He scored more victories and when the war ended he had 28 victories and was awarded the Pour le Merite and the Military Order of Max Joseph.