Abstract: This paper discusses a class of discrete-time recurrent neural networks with linear threshold (LT) neurons for solving traveling salesman problem (TSP). It first addresses the boundedness and complete stability，then gives a theorem to ensure all the networks' iteration solutions to be valid solutions. We also present an algorithm based on such networks with a local escape way. Simulation results illustrate the developed method. Compared with the TSP solutions done by Lotka-Volterra (LV) neural networks, the presented method has better performance.