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Compared with the traditional doubly-fed induction generator (DFIG), the brushless doubly-fed induction generator (BDFIG) eliminates the slip rings and brush gears, which benefits high reliability and low maintenance cost. Thus BDFIG possesses wide application prospects in power generation. With the rapid growing capacity of the power generation system, the instantaneous inrush current becomes a significant factor which is worth of attention. Consequently, this paper analyzes the characteristic of the inrush current of BDFIG under the grid synchronization error. Firstly, the character of the inrush current is analyzed under the s-domain, which helps to understand; Secondly, in order to analyze the character of the inrush current under time-domain, the specific expression of inrush current is obtained by considering amplitude error and phase error, which provides a theoretical basis for seamless transition at the moment of grid connection. Thirdly, the influence of amplitude error or phase error on the inrush current is also investigated based on the obtained expression. Finally, the analysis is verified by both the simulation and experimental results. The work could facilitate future research on suppressing the inrush current of BDFIG, thereby increasing the security and stability of the system.