Based on the generalized Huygens-Fresnel principle and the cross spectral density function, we deduce the expression of intensity distribution of partially coherent off-axis vortex beams propagating in atmospheric turbulence by using the Kolmogorov turbulence spectrum. The effects of off-axial distance, topological charge, waist width, coherent length, transmission distance, turbulence intensity on the intensity distribution are discussed. Simulation results show that the topological charge does not change the position of the dark core. The sign of off-axial distance determines the direction of the dark core movement and the direction in which the intensity is concentrated. The upward movement distance of the core decreases with the increase of the waist width and the coherent length, and increases with the increase of the transmission distance and the turbulence intensity. The spreading of beam increases with the increase of the waist width, the coherent length, the transmission distance and the turbulence intensity.