In this paper, the deterministic annealing and clustering algorithms are applied to the travelling salesman problem, and a heuristic algorithm for the travelling salesman problem is put forward. The method transforms the discrete model of the travelling salesman problem into the continuous model, and the solution of the problem is obtained by solving local optimal solution of a series of problems to minimize the free energy of a physical system which varies with temperature. A simple explicit iterative formula is given. The computation results indicate that this algorithm has good performance.