Lunar Penetrating Radar (LPR) is one of the important scientific systems onboard the Yutu lunar rover for the purpose of detecting the lunar regolith and the subsurface geologic structures of the lunar regolith, providing the opportunity to map the subsurface structure and vertical distribution of the lunar regolith with a high resolution. In this paper, in order to improve the capability of identifying response signals caused by discrete reflectors (such as meteorites, basalt debris, etc.) beneath the lunar surface, we propose a compressive sensing (CS)-based approach to estimate the amplitudes and time delays of the radar signals from LPR data. In this approach, the total-variation (TV) norm was used to estimate the signal parameters by a set of Fourier series coefficients. For this, we chose a nonconsecutive and random set of Fourier series coefficients to increase the resolution of the underlying target signal. After a numerical analysis of the performance of the CS algorithm, a complicated numerical example using a 2D lunar regolith model with clipped Gaussian random permittivity was established to verify the validity of the CS algorithm for LPR data. Finally, the compressive sensing-based approach was applied to process 500-MHz LPR data and reconstruct the target signal’s amplitudes and time delays. In the resulting image, it is clear that the CS-based approach can improve the identification of the target’s response signal in a complex lunar environment.