In numerical simulation of light propagation through the atmosphere with the phase compensation by an adaptive optical system including temporal evolution, such as very long exposure imaging and simulation of the dynamic control process in an adaptive optical system, the generation and application of rectangular turbulence phase screens are critical. But the widely-used spectral approach can only generate square phase screen, and wastes the computational resource because only a rectangular portion of the square phase screen is practically utilized. Furthermore, the spectral phase screen needs low-frequency modification, so that needs more computation. Based on the fractal characteristics of turbulence-distorted wavefront, a new algorithm for generating rectangular turbulent phase screen is proposed. The phase structure function of generated phase screens agrees well with the theoretical one. Compared with existing approaches, the present algorithm shows obvious advantages: simplicity, high efficiency and less computation resource. The generated phase screen agrees with theoretical results from turbulent statistical characteristics, in the low- and high-frequency region.