Ground-penetrating radar (GPR) is one of the most popular subsurface sensing devices and has a wide range of applications, e.g., target detection. It is well known that the target detection process in the GPR is highly affected by clutter. Especially, in the case of landmine detection, since targets are located near the surface, a target signal may be completely covered by the clutter. Thus, clutter reduction must be performed prior to any target detection scheme in the GPR. Singular value decomposition, principal component analysis, and independent component analysis are commonly used for clutter removal. They all aim to decompose the GPR images into subcomponents that represent the clutter and the target separately. In this letter, we propose a sparse model for differentiating the target and the clutter using appropriate dictionaries based on morphological component analysis (MCA). Calculated sparse coefficients and corresponding dictionaries are used to reconstruct the clutter and the target components. Visual and quantitative results validate that the proposed MCA-based method has higher performance than the state-of-the-art clutter reduction methods.