Deep-space laser communication systems commonly use pulse-position modulation (PPM) to improve the energy efficiency of communication and use single-photon detectors for efficient signal reception. In particular, superconducting nanowire single-photon detectors (SNSPD) are one of the most suitable detector choices. In this study, we investigated the performance of high-speed PPM-SNSPD-based deep-space laser communications in terms of the dead time and jitter of SNSPD as well as the trailing phenomenon of high-speed pulsed signals. The photocount characteristics of SNSPD were analyzed. Based on this analysis, we proposed a bias-compensated guard-time PPM symbol synchronization algorithm. Compared with the conventional guard-time symbol synchronization algorithm, the proposed algorithm effectively reduces synchronization errors and improves system error performance.