The methods of power spectrum, Zernike polynomial and Fractal used to generate atmospheric phase screens with the non-Kolmogorov statistics were introduced. Based on the three methods, non-Kolmogorov turbulent phase screens were simulated. Phase structure functions were calculated and compared with the theoretical results. In addition, the accuracy and efficiency of different methods were also analyzed. It shows that phase screen created by FFT method has the drawback of lacking low frequency, by adding subharmonics the phase screen can be compensated which also leading to the decreasing of simulation efficiency; phase screen created by Zernike polynomial method has the drawback of lacking high frequency, by using much more orders of Zernike polynomials the phase screen can be compensated which also leading to the decreasing of simulation efficiency; phase screen created by Fractal method is relatively good at both low and high frequency and the simulation efficiency is also high. In addition, the number of subharmonics and the order of Zernike polynomials under same condition of accuracy are related to the power law of non-Kolmogorov turbulent spectrum. As the spectral power law increases, the number of subharmonics increase and the order of Zernike polynomials decrease, and phase screens created by fractal method are more accurate.