Modular multilevel converter (MMC) consists of a large number of sub-modules (SMs), the operation of which, has direct influence on the total converter substation. So research on the fault characteristic, fast detection and location of the sub-modules are of great significance. In this paper, firstly, the characteristics of MMC SMs short-circuit fault are analyzed and the calculating formula of fault component is deduced, then a method is proposed. Moreover, a novel differential under-voltage detection method is proposed based on SM detection capacitor voltage. Finally, the specific faulty IGBT location is carried out by wavelet transform. Simulations in PSCAD/EMTDC reveal that the proposed method in this paper can calculate accurately the IGBT capacitor voltage after the short-circuit fault of MMC, detect the faulty SM and locate the faulty IGBT precisely and rapidly, which verify the effectiveness and feasibility of the proposed method.