Univ Sci & Technol China, Dept Modern Phys, Hefei 230026, Peoples R China
; Chinese Acad Sci, Inst Theoret Phys, Beijing 100080, Peoples R China
; CCAST, World Lab, Beijing 100080, Peoples R China
; Chinese Acad Sci, Inst High Energy Phys, Beijing 100039, Peoples R China
A supersymmetric vector-like standard model without leptons is suggested to investigate the unification between gauge interactions and gravity under two loop approximation for gauge interactions and one loop string correction for gravitation. It is found that two intermediate mass scales are needed where the lower mass scale may be accessible in laboratory in future and the higher mass scale is of the order of 10(16) GeV.