A faulty submodule (SM) mathematical model-based switch open-circuit fault diagnosis and localization (FDL) method for module multilevel converter (MMC) is investigated in this article, which can diagnosis the faulty switch in time. Initially, the mathematical model is established through the modified switching function of the faulty SM, which can express the real switching state of the faulty SM accurately. Based on the proposed mathematical model, an innovative FDL method for MMC is proposed. The faulty switch is located by comparing the capacitor voltage calculated through the proposed mathematical model with the sampled capacitor voltage value. To enhance the accuracy and anti-interference ability of the model, the capacitance observation method is proposed in the capacitor precharge stage. The proposed FDL method can diagnose and locate faulty switch in any state of the SM, even if the operating state of the faulty SM is the same as that of the normal SM. Single or multiple switch open-circuit faults can be accurately located by this method under either light or heavy load conditions. Finally, the mathematical model and FDL method are verified through simulation and experiment.