Multi-terminal voltage sourced converter (VSC)-based high voltage direct current (HVDC) system composes of a number of VSCs connected to an HVDC grid (or dc grid). The dc grid is often configured by cable interconnections between converter stations, thus imposing resonance issues affecting harmonic interaction in the system. Based on the harmonic transfer characteristics of VSC and HVDC systems, the appearance and the interaction of inter-harmonics in the multi-terminal VSC-based HVDC system are analyzed. Simulation models are built and implemented using SimPowerSystems in MATLAB. The simulation results show that, a series of inter-harmonics are produced and tend to be dominant in low-frequency range. Especially in the dc grid, the inter-harmonic transfer can be magnified due to inter-harmonic resonances. The complex resonance issues in the dc grid are investigated in combination with interaction through the VSC, it is beneficial to harmonic filter designs as well as other harmonic mitigation methods.