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The shortest path problem is one of the classical combinatorial optimization problems having widespread applications in a variety of planning and designing contexts. In this paper, a hysteretic transiently chaotic neural network model (HTCNN) for solving the shortest path problem has been presented. By using hysteretic activation function which is multi-valued, adaptive, and has memory, HTCNN has higher ability of overcoming drawbacks that suffered from the local minimum and converge to the optimal solution quickly. From the simulation results, obtained under 5 nodes and 10 nodes networks topologies, it can be concluded that the proposed model has higher ability to search for globally optimal and has higher searching efficiency in solving the shortest path problem.