This paper examines the transient synchronization stability (TSS) of an island 100 % renewable power generation (RPG) system that is connected to the Zhangbei multi-terminal direct current (MTDC) system. A large-signal model of the system is derived, based on which an analytical criterion for evaluating the TSS of the system is proposed. From the proposed TSS criterion, the current injection of the RPG, the current injection of the MMC, the parameter settings of the PLL, and the fault ground resistance and distance are identified and examined as four key factors affecting the system TSS. In addition, analysis in the paper highlights the importance considering the reactive current generated by the RPG during the fault, because excessive reactive current may causes the instability of the island 100 % RPG system. To demonstrate and evaluate the proposed TSS criterion and the analytical conclusions made, study cases to examine the TSS of the island 100 % RPG system connected to the Zhangbei MTDC are presented in the paper.