Single-line to ground fault occurring on the grid side causes certain drops in alternating current (AC) voltage. At this time, the modular multilevel converter (MMC) system is able to achieve low voltage ride-through under fault with the injection of reactive current. However, the grounding impedance affects the topology of the whole system, thus leading to couplings among the sequence networks. Therefore, modeling and stability analysis of MMC system is of vital significance in this case. The equivalent model of MMC AC system disturbed by single-line to ground fault is established, and the process of fault ride-through with the mixed injection of dual-sequence reactive current is analyzed. Then, based on internal dynamic characteristics of sub-module capacitor voltage and arm current of MMC, the small signal model is established. The influence of impedance parameters and current couplings on small signal stability of MMC are analyzed by using the root-locus method on the basis of system instability mechanism. Finally, a 21-level MMC simulation model is built in PSCAD/EMTDC and the simulation results show that the decrease of the grid impedance or the increase of the ground impedance makes the system tend to be unstable. And the injection of negative sequence reactive current expands the stable region of positive sequence reactive current.