A mathematical model of two-level voltage sourced converter（VSC） HVDC system based on the switching function method is introduced. The paper analyzes the harmonic characteristics of VSC with sinusoidal pulse width modulation（SPWM）， points out that the zero sequence harmonics at the carrier frequency are the main harmonic component at the AC side. The zero sequence harmonic current is converted into unbalanced DC side harmonic currents at the same frequency by multiplying the fundamental component of the switching functions. The DC side grounding method is found to determine the path of the unbalanced DC side harmonic currents. With both DC sides of the VSC HVDC system grounded， the unbalanced DC side harmonic currents will circulate at local area via the DC side grounding point and the AC side high-pass filter grounding point. Otherwise， the unbalanced DC side harmonic currents will flow along the DC cables， and cause a series of problems. The results are verified by a test system established in PSCAD/EMTDC. It concludes that the DC sides of both terminals need to be grounded in a VSC HVDC system.