In order to solve the problem of high and low voltage fault ride-through of modular multilevel converter （MMC） under weak grid，a multi-link control strategy including capacitance voltage balancing control of integral，phase-to-phase and upper and lower bridge arm，improved phase-locked loop （PLL） and multi-resonance control is proposed. Firstly，the pre-filtering stage of the double second-order generalized integrator （DSOGI） is improved，and nonlinear proportional integral （PI） control is adopted in the PLL. Secondly，a capacitance voltage equalization control method based on the power redistribution for MMC under weak grid is proposed，and the active power redistribution of the submodule is realized by controlling the DC component of the bridge arm current. Then，considering the inconsistency of the upper and lower arm losses or asymmetrical parameters，the traditional voltage equalization control of the upper and lower bridge arm is improved by adopting the method of the active power redistribution of the upper and lower bridge arm. The simulation results show that the proposed control strategy realizes the uninterrupted operation of the system under the fault ride-through，solving the problem of inaccurate phase and frequency detection of PLL during high and low voltage ride-through and the current imbalance caused by three-phase voltage imbalance.