Precocity, stagnation and phenomenon of long time convergence often emerge from classical genetic algorithm or ant colony algorithm. At the same time, they have different features of convergence in each algorithm. So, a coevolutionary model is presented based on genetic algorithm and ant colony algorithm, which runs one of the above two algorithm and exchanges another by estimating the state of their running. In order to search optimal result of problem, genetic algorithm and ant colony algorithm can run conjunctly in the model. Through the experimentation on symmetric and asymmetric TSP, the outcome shows that compared with other algorithm, the algorithm of the model takes a great improvement in the convergent speed, result optimization and also the avoidance of the precocity and stagnation.