To address the issue of circulating current suppression in parallel common DC-bus multi-inverter systems, this paper analyzes the circulating current loop and excitation source characteristics of a three-phase four-leg inverter parallel system. Based on this analysis, the circulating current oscillation and low-frequency circulating current cumulation effects caused by introducing virtual impedance into the virtual synchronous generator (VSG) control strategy are investigated. On this basis, a circulating current suppression strategy based on sliding mode control (SMC) is proposed. The proposed strategy is designed according to Lyapunov stability theory. Specifically, an exponential reaching law is introduced into the control loop to generate an equivalent reverse excitation source, thereby suppressing instantaneous circulating currents. Meanwhile, a proportional negative-feedback term based on the derivative of the sliding surface is employed to adjust the modulation wave amplitude gain, thereby mitigating low-frequency circulating currents. Under typical operating conditions with carrier frequencies of 15 kHz and 20 kHz and mismatched filter parameters, simulation results show that the peak zero-sequence circulating current is reduced from 1.6 A to 0.9 A, effectively suppressing the cumulation effect of low-frequency circulating currents. Experimental tests on a hardware platform further demonstrate a reduction in the circulating current peak from 5 A to 2.5 A, thereby validating the feasibility and effectiveness of the proposed strategy in practical engineering applications.