Adem Grabovci was born in the village of Staraduran, Pejë. He was a political prisoner from 1984 to 1989 and pioneered the reconciliation of blood feuds in 1990. After fleeing to Switzerland, he served as chairman of the People's Movement of Kosovo branch in Switzerland and was a member of the Popular Movement for the diaspora. He was one of the founders of the fund "Homeland Calling" () which collected financial contribution from Albanian diaspora during the war. He was one of the founders of the KLA, and a member of the General Staff of the KLA.