The shortest path problem is an important issue in communication networks which is used by many practical routing protocols. The aim of this paper is to present an intelligent model based on Hopfield neural networks (HNNs) for solving shortest path problem and implement that on Field Programmable Gate Arrays (FPGAs) chips. The Cyclone Π-EP2C70F896C6 FPGA chip from ALTERA Inc. is considered for hardware implementing and VHDL language is employed for hardware description. The synthesizing results show the proposed architecture of neuron is more efficient than relevant neuron model for chip area utilization and consequently improving the maximum operating frequency and power consumption. The proposed router core is employed to find shortest paths in ring, star and mesh communication networks and the results demonstrate the efficiency and superiority of proposed core.