Abstract: The convergence of genetic algorithm （GA）, especially the consequence of crossover operator, is devoid of theoretic analysis. When the system dynamic analysis of running mechanism of GA is applied, the constringency of GA can be discussed when mutation operator is omitted. An explicit definition of local peak is shown, and the existence condition of local peak is given. It is proved that the GA is constringent at the neighbor of its local peak. The theoretical evidences of some improvements on GA are given, which points out the way forward for improving GA’s performance.