In recent years, Long-Term Evolution Vehicle-to-Everything (LTE-V2X) communication technology has received extensive attention. Timing synchronization is a crucial step in the receiving process, addressing Timing Offsets (TOs) resulting from random propagation delays, sampling frequency mismatches between the transmitter and receiver or a combination of both. However, the presence of high-speed relative movement between nodes and a low antenna height leads to a significant Doppler frequency offset, resulting in a low Signal-to-Noise Ratio (SNR) for received signals in LTE-V2X communication scenarios. This paper aims to investigate LTE-V2X technology with a specific focus on time synchronization. The research centers on the time synchronization method utilizing the Primary Sidelink Synchronization Signal (PSSS) and conducts a comprehensive analysis of existing algorithms, highlighting their respective advantages and disadvantages. On this basis, a robust timing synchronization algorithm for LTE-V2X communication scenarios is proposed. The algorithm comprises three key steps: coarse synchronization, frequency offset estimation and fine synchronization. Enhanced robustness is achieved through algorithm fusion, optimal decision threshold design and predefined frequency offset values. Furthermore, a hardware-in-the-loop simulation platform is established. The simulation results demonstrate a substantial performance improvement for the proposed algorithm compared to existing methods under adverse channel conditions characterized by high frequency offsets and low SNR.