In order to investigate the evolution of beam wander of partially coherent crescent beams in non-Kolmogorov turbulence, the extended Huygens-Fresnel principle was used and the corresponding analytical expressions were obtained. Numerical simulation was carried out by using MATLAB. The results show that, in the non-Kolmogorov turbulence, beam wander of partially coherent crescent-like beams decreases with the increase of anisotropic parameters, the increase of turbulent inner scale, the decrease of turbulent outer scale and the decrease of structural constants respectively. Compared with isotropic turbulence, anisotropic turbulence has little effect on beam wander. Off-axis distance of the maximum intensity position of crescent-like beam increases with the increase of wavelength and beam order respectively. It decreases with the increase of coherence length. Off-axis characteristic at the position of the maximum intensity is beneficial for crescent-like beams to transmit around obstacles. The obtained conclusions have some reference value for practical optical communication.