Abstract: Genetic algorithm has the ability of quickly and stochastically global searching, however, it can not make good use of enough output information for systems. Ant system is a parallel-process and distributive-forward system with a relatively slow velocity for providing the solution. Combining genetic and ant algorithms can increase the merits each other. Based on the idea above. the model and method from the combination of genetic and ant algorithms are proposed, and the convergence of the method based on the Markov theory is analysed. Moreover, the conclusion can be drawn that the solution sequence is monotonically decreasing and convergent. The experiment and analysis are carried out for the case-S of TSP30 and CHNl44 on an NP-hard problem. The results of simulation show that not only the mixed algorithm is a step-by-step convergent process, but also its velocity and effect of solving are quite satisfactory.