As a new type of voltage source multilevel converters, the Modular Multilevel Converter (MMC) has strong expansibility, high output voltage quality, low harmonic content, and it has shown the great prospect of application. This paper firstly introduces the topology structure and operation principle of MMC-HVDC. Then, the internal and external faults are analyzed respectively through the fault added state network, and a protection strategy is given by extracting the fault component of current and voltage fault component by two-order differential method. According to the fault network analysis, when the fault occurs in the DC line, the polarity of the current fault component is the same. When the fault occurs outside the DC line, the polarity of the current fault component is opposite. Therefore, the internal and external faults can be identified according to whether the polarity of the current fault component is identical by extracting the current fault component with two derivative identification. In addition, according to the fault network analysis, when the internal fault occurs in the DC line, voltage fault component has the same polarity while unipolar fault occurs in the DC lines, and voltage fault component has opposite polarity while bipolar fault occurs in the DC lines. Therefore, according to the polarity of the voltage fault component, it can recognize fault polarity and extract the voltage fault component by two-order differential method to identify fault polarity. Finally, simulation model of MMC-HVDC is established in PSCAD. Simulation results are given to verify the correctness of the fault analysis and protection methods. This work is supported by Key Support Projects of National Natural Science Foundation of China (No. U1766209) and National Natural Science Foundation of China (No. 51777166).