Accurately generating the phase screen (PS) is a key step to numerical simulation of the atmospheric turbulence. According to the statistical characteristics of turbulence, a new method called random unit expansion mainly focusing on the scale distribution randomness and small scale phase fluctuation of turbulence is induced by use of the phase structure function (PSF). Based on the PS generated, Kolmogorov atmospheric turbulence model is obtained. Expansion result shows that the phase structure function derived from the simulation is very close to the ideal one. Compared with power spectrum method, performance in low-frequency part is better. Meanwhile, as the grid number of PS increases, characteristic in high frequency part appears obviously and gradually closer to the ideal function. To evaluate the accuracy of the atmospheric turbulence numerical model, scintillation ratio is computed. In the condition of weak and moderate turbulence, the simulated result agrees with theoretical one, while to the strong turbulence, max relative error will be about 40%.