Based on power spectral density method, the uniform sampling leading to the leakage of low frequency in atmosphere phase screens is analyzed. A new method - non-uniform sampling is proposed. The non-uniform sampling is modeled. The covered sampling frequency regions and the powers of single sampling region by the two sampling methods are discussed and compared. The new method proves to be effective and feasible. For the Kolmogorov spectrum of atmospheric turbulence, the numerical simulation phase screens are generated by the two sampling methods. The simulation results show that the random phase screens generated by the non-uniform sampling method under the condition of increasing neither sampling number nor computation burden, possesses rich high and low frequency information.