Recently and successfully, the Chang’E-5 (CE-5) lander was launched on a mission to bring 1.731 kg of lunar soil back to Earth. To investigate various compositions of lunar regolith, we apply the Lunar Regolith Penetrating Radar (LRPR) as the same scientific payload installed on the CE-5 lander. Based on the high-accuracy imaging technique, we achieve subsurface imaging to process LRPR-measured data collected from the lunar-like exploration tests in our laboratory. In this paper, we propose the pseudo-spectral time-domain (PSTD) method as the underlying code to implement the reverse-time migration (RTM) method and restore the uncertain subsurface area. With the significant advantage of lower spatial sampling density, the PSTD-RTM method not only saves major computational resources, but also rapidly confirms the object prediction in the effective imaging area. To further analyze the LRPR measured data, we employ the spectrum window to remove high- and low-frequency noise, and thus improve imaging visibility to some extent. The imaging results in this paper can prove the reliability and efficiency of the PSTD-RTM method for subsurface discoveries in planetary exploration.