The instability issues of phase-locked loop (PLL) may have an adverse impact on the stable operation of modularmultilevel-converter-based high voltage DC system (MMC-HVDC), especially the strength of the adjacent AC system is very weak with a low short circuit ratio (SCR). However, there is no consensus about how weak the system is when the influence of PLL cannot be ignored. To address the gap, this paper firstly establishes the small-signal models of the MMC with and without the dynamic of the PLL, respectively. Then, mechanism analysis of the influence of the strength of the AC system on the stability of the MMC-HVDC system. According to the comparative analysis, the recommendation SCR boundary that the dynamics of the PLL can not be ignored is given. Finally, electromagnetictransient simulations of an LCC-MMC system are conducted to validate the above analysis.