The analytical expression of off-axis hollow Gaussian–Schell model vortex beam (HGSMVB) generated byanisotropic Gaussian–Schell model source is first introduced. The evolution properties of off-axis HGSMVB propagat-ing in turbulent atmosphere are analyzed. The results show that the off-axis HGSMVB with smaller coherence length or propagating in stronger turbulent atmosphere will evolve from dark hollow beam into Gaussian-like beam with a larger beam spot faster. The beams with different values of integer order N or the position for hollow and vortex factor R will have almost the same Gaussian-like spot distribution at the longer propagation distance.