To solve the problem that a Modular Multilevel Converter (MMC) outputs harmonic current affected by background harmonics of a power grid, a suppression strategy is proposed. The output voltage of an MMC when there are background harmonics is obtained by calculating the energy fluctuation function of sub-modules, and then the generation law of background harmonic current at the MMC grid side is analyzed. A multi-channel signal separator is designed by using a cross decoupling complex filter to separate and extract MMC grid-side harmonic signals. An MMC mathematical model is established for separated harmonics, and a harmonic current suppressor is designed based on this. The theoretical analysis and suppression strategy are verified by building a double terminal HVDC transmission simulation model. Simulation results show that the generation law of background harmonic current at the MMC grid side is consistent with the theoretical analysis, and the proposed suppression strategy can effectively reduce the background harmonic content of MMC grid-side current. This work is supported by the Science and Technology Project of the Headquarters of the State Grid Corporation of China (No. 52130419000M).