The minimum vertex cover problem is a classical problem in combinatorial optimization and has a wide range of values in real life. The problem of the minimum vertex cover and the maximum independent set is actually the equivalence problem in the graph theory. In this paper, the maximum independent set angle and design a maximum independent set algorithm for solving the planar graph is formed, according to characteristics of the maximum independent set, and then the minimum vertex cover is obtained. After many experiments, the results show adequately that the algorithm presented in the thesis is correct and effective.