It is well known that the traveling salesman problem (TSP) is one of the most studied NP-complete problems, and evolutionary technique such as simulated annealing has mostly been used to solve various NP-complete problems. In this paper, a two-stage simulated annealing (two-stage SA) algorithm is proposed to solve the TSP, and the two-stage SA algorithm is made up of two stages. In the first stage, a simple simulated annealing (simple SA) algorithm is proposed to obtain some appropriate solutions or closed tours. In the second stage, an effective simulated annealing (effective SA) algorithm is proposed to obtain solutions with good quality based on the solutions or closed tours obtained by the simple SA algorithm. To assess the effectiveness of the two-stage SA algorithm, simulations were carried out on 23 benchmark TSP instances. The simulation results show that the two-stage SA algorithm can obtain solutions with better quality than four recent algorithms such as ant colony optimization algorithm, self-organizing maps algorithm, particle swarm optimization algorithm and constructive optimizer neural network algorithm.