The fault probability of sub-modules in modular multilevel converter (MMC) stays at a high level, fast and precise diagnosing and isolating the faulted sub-modules are critical for MMC to improve the operation conditions of converter and avoid unnecessary outages. Based on analysis of open-circuit fault characteristics of insulated gate bipolar transistor (IGBT) of sub-modules, a sliding mode observer is constructed to observe arm current and detect swiftly open-circuit fault in IGBT sub-module. By using the difference and changing rate between the measured value and the calculated value of arm current, fault type of the sub-module can be distinguished, relevant part of the sub-modules is selected according to the types of fault, then by calculating the ratio of the actual value against the theoretical value of the current flowing through sub-modules, the faulted sub-module can be located. Simulation on an MMC-HVDC system established on PSCAD/EMTDC shows that the proposed fault diagnosis method can reduce the computation of fault location effectively, detect and locate IGBT open-circuit fault accurately and swiftly.