This paper presents a coupled neural network, called output-threshold coupled neural network (OTCNN), which can mimic the autowaves in the present pulsed coupled neural networks (PCNNs), by the construction of mutual coupling between neuron outputs and the threshold of a neuron. Based on its autowaves, this paper presents a method for finding the shortest path in shortest time with OTCNNs. The method presented here features much fewer neurons needed, simplicity of the structure of the neurons and the networks, and large scale of parallel computation. It is shown that OTCNN is very effective in finding the shortest paths from a single start node to multiple destination nodes for asymmetric weighted graph, with a number of iterations proportional only to the length of the shortest paths, but independent of the complexity of the graph and the total number of existing paths in the graph. Finally, examples for finding the shortest path are presented. This paper presents a coupled neural network, called output-threshold coupled neural network (OTCNN), which can mimic the autowaves in the present pulsed coupled neural networks (PCNNs), by the construction of mutual coupling between neuron outputs and the threshold of a neuron Based on its autowaves, this paper presents a method for finding the shortest path in shortest time with OTCNN. The method presented here features much fewer neurons needed, simplicity of the structure of the neurons and the networks, and large scale of parallel computation. It is shown that OTCNN is very effective in finding shortest paths from a single start node to multiple destination nodes for asymmetric weighted graph, with a number of iterations proportional to to length of the shortest paths, but independent of the complexity of the graph and the total number of existing paths in the graph. Finally, examples for finding the shortest path are presented.