An improved subharmonic method to generate atmospheric turbulence phase screen was introduced. The low frequency phase screen is specifically designed to quickly achieve adequately sampling in low frequency portion of power spectrum. To evaluate the accuracy of the proposed method, the phase structure function of phase screen generated by using this method is calculated and compared with the theoretical Kolmogorov structure function. The accuracy of the simulated phase screen can be improved with the increase of subharmonics. In addition, comparison between the improved subharmonic method and other four phase screen generation methods (standard fast Fourier transform method, subharmonic method, Zernike polynomials method and random mid-point displacement method) is also carried out. The comparative results show that the phase structure function for the improved subharmonic method matches very closely that of Kolmogorov turbulence theory, and it is the best one in comparison with those of other four phase screen generation methods.