Abstract: Solving Hamilton-circle on a complete graph is a typical combinatorial optimization problem. Genetic algorithm is a good way to solve such an NP problem. In this paper, the basic genetic algorithm is improved. Particularly, the greedy optimization ideas are applied to the selection and mutation operation in order to obtain global optimal solutions with the algorithm. In the MATLAB environment, the algorithm was simulated to implement classical Hamilton circle- TSP (travelling salesman problem) and the results verify the feasibility and correctness of the algorithm.