The voltage source converter based multi-terminal high-voltage direct current (VSC-MTDC) system has attracted much attention because it can achieve the interconnection between AC grids. However, the initial phases and short-circuit ratios (SCRs) of the interconnected AC grids cause the steady-state phases (SSPs) of AC ports in the VSC-MTDC system to be different. This can lead to issues such as mismatches in multiple converter reference frame systems, potentially causing inaccuracies in stability analysis when this phenomenon is disregarded. To address the aforementioned issues, a multi-port network model of the VSC-MTDC system, which considers the SSPs of the AC grids and AC ports, is derived by multiplying the port models of different subsystems (SSs). The proposed multi-port network model can accurately describe the transmission characteristics between the input and output ports of the system. Additionally, this model facilitates accurate analysis of the system stability. Furthermore, it identifies the key factors affecting the system stability. Ultimately, the accuracy of the proposed multi-port network model and the analysis of key factors are verified by time-domain simulations.