The model of beam wander of partially coherent dark hollow beam (PCDHB) is deriv ed based on the theory of second-order moments and non-Kolmogorov turbulence s pectrum.The effect of the non-Kolmogorov parameters (the generalized refractive index structure parameter C²_n,the generalized exponent parameter β,the inner scale of tur bulence l_0and the outer scale of turbulence L₀) and beam parameters (beam waist sizes ω₀,the transverse coherence length σ_0and the wave length λ) on the root-mean-square (rms) beam wan der (BWw) and relative beam wander (BWr) is studied. The results show that beam wander of PCDHB increases with the increases of tota l propagation path length (L_z) and the generalized exponent paramete r.The rms beam wander increases with the increases of generalized refractive index structure parameter and the outer scale of turbulence.The relative beam wander increases with increases of the transverse coherence length and the wavelength.The relative beam wander increases with increases of beam w aist sizes for the case of L_z＞4 km.It also indicates that the influe nce of the turbulence on the beam wander and beam spreading is different under the same conditions.The influence of turbulen ce on beam spreading is getting worse with the increases of L_z.