Ground penetrating radar (GPR) uses electromagnetic waves to image, locate, and identify changes in electric and magnetic properties in the ground. The received signal comprises not only the target echoes but also strong reflections from the rough, uneven ground surface, which impair subsurface inspections and visualization of buried objects. In this paper, a background clutter mitigation and target detection method using low-rank and sparse priors is proposed for GPR data. The radar signal is decomposed into the sum of a low-rank component and a sparse component, plus noise. The low-rank component captures the ground surface reflections and background clutter, whereas the sparse component contains the target reflections. The effectiveness of the proposed method is evaluated on real radar signals collected from buried landmines and improvised explosive devices. The experimental results show that the proposed method successfully removes the background clutter and estimates the target signals.