Isolation of the fault DC lines during the initial fault period after is a major challenge in the multi-terminal DC (MTDC) system based on voltage source converter (VSC). Existing protection schemes and fault analysis methods are mainly based on the numerical simulations, which are lack of the reliable theoretical analysis. In this paper, a high frequency equivalent model of VSC based MTDC system is proposed for the fault current calculation of the system in the initial stage of DC fault. In the proposed model, the parallel connected capacitors of VSCs are regarded as short-circuited, and the initial fault current calculation can be reduced as a reduced-order RL and RLC circuit. In addition, the errors between the transient fault current calculation based on the high frequency equivalent model and the fundamental RL model are also evaluated. Numerous simulation are studied based on PSCAD/EMTDC. The results demonstrate that the proposed high-frequency equivalent model can be utilized for initial DC fault analysis of VSC based MTDC system under different fault locations and the accuracy of results can meet the engineering requirements.