Although ant colony algorithm for the heuristic solution of hard combinational optimization problems enjoy a rapidly growing popularity, but little is known about its convergence properties. Based on the introduction of the basic principle and mathematical model, a novel approach to the convergence proof that applies directly to the ant colony algorithm is proposed in this paper. Then, a MATLAB GUI- based ant colony algorithm simulation platform is developed, and the interface of this simulation platform is very friendly, easy to use and to modify. Since ant colony algorithm for the heuristic solution of hard combinational optimization problems enjoy a rapidly growing popularity, but little is known about its convergence properties. Based on the introduction of the basic principle and mathematical model, a novel approach to the convergence proof that applies directly to the ant colony algorithm is proposed in this paper. Then, a MATLAB GUI-based ant colony algorithm simulation platform is developed, and the interface of this simulation platform is very friendly, easy to use and to modify.