Vortex beam has potential applications in free space optical communication because of its capacity of data transmission. Therefore, it is necessary to study the propagation characteristics of vortex beams in atmospheric turbulence. When the vortex beam propagates in the atmospheric turbulence the beam drift will occur, which has a great influence on the free space optical communication. In this paper, the beam drift of vortex beams with coma and spherical aberration transmitted in atmospheric turbulence is studied by using multi-phase screen and Fourier transform method. The numerical results show that as the transmission distance increases, the effects of both coma and spherical aberration on the beam drift are enhanced. The larger the transmission zenith angle and the coma coefficients, the greater the beam drift of the vortex beam is. However, the beam drift decreases with spherical aberration coefficient increasing. When the zenith angle and the transmission distance are both unchanged, the beam drift of the both vortex beams decrease with topological charges increasing. The influence of coma aberration on beam drift is bigger than that of spherical aberration.