Abstract: In 5G communication systems, the first step for users to establish a connection with Low Earth Orbit (LEO) Satellites is to perform a cell search and complete initial time-frequency synchronization. However, the rapid movement of LEO satellites can cause significant Doppler frequency shifts, leading to constellation rotation of the received signal, thereby reducing the correlation peak of the synchronization signal and affecting the performance of time-frequency synchronization. In this article, combining the characteristics of 5G primary synchronization signals (PSS), various initial time-frequency synchronization algorithms were proposed for the situation under the influence of large Doppler frequency shifts. And the multiple PSS-based joint time-frequency synchronization algorithms were analyzed from the aspects of time synchronization performance, the estimation accuracy of the frequency offset and the complexity. Finally, the effectiveness and robustness of the proposed initial time-frequency synchronization algorithm were demonstrated based on simulation analysis method, obtaining relativity data under the influence of large Doppler frequency shifts.