Fault reconfiguration is an effective measure for restoring power supply when a fault occurs in a shipboard power system. Considering the special working conditions, it is necessary to consider the reliability and power quality of important loads in fault reconfiguration. Therefore, a fault reconfiguration strategy for shipboard power system considering reliability constraints is proposed. Graph theory is used to establish a correlation model between power supply reliability and power network topology, and a depth search algorithm is used to traverse all power supply paths of important load nodes. Based on second-order conic programming, a convex optimization model for fault reconstruction is established, and the model is further transformed into a mixed integer linear programming model by a polyhedral approximation algorithm to accelerate the solution. Based on system simulation and comparative analysis, the results show that the proposed algorithm can quickly obtain the global optimal solution, and the fault reconfiguration strategy can ensure the power quality and power supply reliability of important loads. This work is supported by National Key Research and Development Program of China (No. 2017YFC0307800).