The laser-pumped X-ray detection method is a crucial tool for investigating molecular dynamics, allowing researchers to study ultrafast structural changes within materials. This method demands extremely high precision in the synchronization and delay timing between the pump pulse and the probe pulse. In this study, we explored picosecond (ps)-level clock synchronization control between synchrotron radiation X-ray pulses and femtosecond (fs) laser pulses at the BL05U (d-Line) of the Shanghai Synchrotron Radiation Facility (SSRF). Utilizing the X-ray pulses generated by the 40 ps/0.3 mA electron beam bunch from the SSRF and femtosecond laser pulses with high repetition rates and high emission power, we conducted synchronization experiments. A custom-developed picosecond time synchronization control system and a high dynamic range X-ray streak camera with picosecond time resolution were used as detectors, enabling ultra-precise time synchronization monitoring of X-ray and laser pulses. This setup achieves higher time resolution without the need for photodiodes and oscilloscopes. Using the X-ray pulses as a stationary reference frame, we adjusted the clock synchronization control system to delay the laser pulses and measured their relative timing changes with the X-ray streak camera. The experiments demonstrated a time resolution better than 10 ps, providing a foundation for achieving 60 ps time resolution in laser-pumped X-ray detection experiments at the SSRF.