The Travelling Salesman problem（TSP） is studied using Hopfield neural network（HNN） in this paper.A new algorithm is proposed by simplifying energy function

and the feasibility of the algorithm is analyzed.The analysis is based on the geometry of the subspace set up by the degenerated eigenvalues of the connection matrix.A large number of simulation results show that the algorithm has the advantage of avoiding most local energy minima with the optimum or near-optimum solution and fast speed of convergence.