Based on the non-Kolmogorov turbulence spectrum and the theory of second moments, a general analytical expression of beam wander model in non-Kolmogorov turbulence is derived. The results indicate that the beam wander depends on turbulence parameters including the generalized exponent parameter α, refractive index structure parameter C2n, turbulence outer scale L0, turbulence inner scale l0 and initial second moments of laser beam at the input plane. Taking the partially coherent anomalous elliptical hollow Gaussion beam (PCAEHGB) as an example, we simulate the root-mean-square (RMS) beam wander Bw and the relative beam wander Br numerically. It shows that Bw and Br increase with the increasing generalized exponent parameter, refractive index structure parameter, turbulence inner scale, turbulence outer scale, coherence length and beam waist radius. The results also indicate that Bw≈0.22 m when C2n=10-14 m3-α and the total propagation path length L=10 km, and Br reaches the maximum value when L≈5 km. Furthermore, PCAEHGB is less affected by turbulence than Gaussian-Schell model beam under the condition of the same parameters.