The transformer inrush current has been a potential threat in wind farms connected modular multilevel converter based high-voltage direct current (WF-MMC-HVDC) system due to the low overcurrent capability of power electronic devices. To investigate this issue, this paper develops a complete harmonic state space (HSS) model of the WF-MMC-HVDC system containing saturable transformers. The severity of the inrush current is investigated under different transformer configurations and the result is compared with EMTP simulations. More importantly, key factors that influence inrush current characteristics in a WF-MMC-HVDC system are studied using the single-input single-output impedance model derived from the linearized HSS model. The results indicate that wind farms have a minor impact on the inrush current characteristics, whereas V/F controlled modular multilevel converter (MMC) reduces its output voltage during transformer energization, thereby mitigating the severity of the inrush current. The severity of the inrush current largely depends on the resonance point determined by the transmission line. In the case of offshore WF-MMC-HVDC system, long submarine cables may cause severe harmonic amplifications and even do not attenuate for a long time.