Answer:
Tsehafi Tizazu Aklilu Habtewold ( At the time of Emperor Hailesilassie I)
Fikresilassie Wegderes ( At the time of DERG or Ethiopian People Democratic Republic)
Tamrat Layne ( At the time of EPDRF or Ethiopian People Democratic Republic Front)
Meles Zenawi (EPDRF)
Hailemariam Desalegn (EPDRF)
Abiy Ahmed (EPDRF or the now Prosperity Party)
By the way these are not the only Prime ministers of Ethiopia these are the ones I remember now.