In this paper, we constructed mathematical models for genetic algorithm (GA) and explored the searching process of genetic algorithm with statistical methods. Both two-dimensional and multidimensional benchmark functions were used to test the GA. Every group of the searching pace of GA performs power law distributions, even that the data is drawn from non-convergence cases. L1vy flight search patterns are proved to play an important role in the process. The efficiency of optimization process has something to do with the parameters of power law distributions. More interesting results and conclusions are given in the paper.