The nonlinear power loads are increasing with the rapid development of the modern industry, resulting in a large number of harmonics and inter-harmonics appear in the power grid, and the power grid environment is increasingly complex, which poses a new challenge to the safe and stable operation of grid-connected inverter. In this paper, the mechanism of the grid-connected inverter oscillation induced by inter-harmonic voltage under complex grid conditions is analyzed in detail, and the corresponding oscillation suppression measures are proposed. Firstly, the characteristics of the inter-harmonics in power grid and the influence of the inter-harmonic on the output power of the grid-connected inverter are introduced. It is found that the inter-harmonics will lead to continuous periodic fluctuations in the output active power of the inverter. Then, the mechanism and characteristics of the oscillation induced by periodic power fluctuation are revealed from the perspective of forced oscillation by a reduced-order inverter model with dominant oscillation modes reserved. On this basis, it is found that the amplitude of the forced oscillation is strongly correlated with the damping of the dominant oscillation modes, and then, an active damping in the DC-link voltage control loop is proposed to suppress the forced oscillation. Finally, the correctness of the oscillation mechanism analysis and the effectiveness of the oscillation suppression strategy are verified by simulations.