The earliest football played in Asbach was in 1911 and prior to World War I two clubs emerged. Spielvereinigung Asbach and Sportverein Germania Asbach were youth clubs that disappeared as a consequence of the war. A number of short-lived sports and gymnastics clubs came and went between 1922 and the formation on 5 August 1928 of Sportverein Asbach. This club also struggled early on, but managed to persevere. By 1936 SV had a number of local honours to its credit and was finally able to establish its own ground.
SVA long played in the shadow of Hessen Bad Hersfeld, but after a 1993 title in the Bezirksoberliga Fulda (V) has become a fixture in the Landesliga Hesse-Nord (V). Following a second place finish in the Verbandsliga Hessen-Nord (VI) in 2008–09, SVA was promoted to the Hessenliga but lasted for only one season before going down again.