Neural network (or parallel distributed processing) models have been shown to have some potential for solving optimisation problems. Most formulations result in NP-complete problems and solutions rely on energy based models, so there is no guarantee that the network converges to a global optimal solution. In this paper, we propose a non-energy based neural shortest path network based on the principle of dynamic programming and least take all network. No problem of local minima exists and it guarantees to reach the optimal solution. The network can work purely in an asynchronous mode which greatly increases the computation speed.