To adapt to the large-scale access of new energy to the power grid, an MMC-HVDC is increasingly widely used, and China's power grid has initially become an AC-DC hybrid power grid. When the AC system fails, the characteristics of short-circuit current provided by an MMC system change significantly compared with a traditional synchronous generator. First, this paper analyzes the change of fault characteristics. Because of the limited amplitude of fault current and infinite negative sequence impedance on the MMC side, the amplitude and phase of fault current are different from those on the AC side. The paper finds that when there is an increase of the current angle on both sides in the case of a fault in the transmission line, the differential current will be reduced and the braking current will be increased. Also the sensitivity of protection will be reduced or even the protection will not be activiated. This paper proposes an improved scheme for the differential protection criterion: the zero-sequence current, the negative-sequence current and the positive-sequence current mutation are respectively used to form auxiliary criteria to improve the sensitivity of the current differential protection during ground faults and phase-to-phase short-circuits. This improves the reliability of the differential protection in the AC power grid with an MMC system. Finally, the feasibility of the proposed scheme is verified by simulation. This work is supported by the Key Project of National Natural Science Foundation of China (No. 51637005).