To generate time-evolving atmosphere turbulence in real time, a phase-generating method for our liquid-crystal (LC) atmosphere turbulence simulator (ATS) is derived based on the Fourier series (FS) method. A real matrix expression for generating turbulence phases is given and calculated with a graphic processing unit (GPU), the GeForce 8800 Ultra. A liquid crystal on silicon (LCOS) with 256x256 pixels is used as the turbulence simulator. The total time to generate a turbulence phase is about 7.8 ms for calculation and readout with the GPU. A parallel processing method of calculating and sending a picture to the LCOS is used to improve the simulating speed of our LC ATS. Therefore, the real-time turbulence phase-generation frequency of our LC ATS is up to 128 Hz. To our knowledge, it is the highest speed used to generate a turbulence phase in real time.