Based on the biologic agamogenesis mechanism, the agamogenetic algorithm (AGA), which is similar to classical genetic algorithms except the agamogenesis and highly converging speed, is presented to solve the optimization problems. In order to solve the traveling salesman problem (TSP) by AGA, one agamogenetic operator R-Edge and one mutation operator NI-Dot are given by introducing the conception of the relative distance between cities. The validity of the AGA to solve the traveling salesman problem is shown by simulative experiments.