We propose an effective technique for estimation of targets by ground penetrating radar (GPR) using model-based compressive sensing (CS). We demonstrate the technique's performance by applying it to detection of buried landmines. The conventional CS algorithm enables the reconstruction of sparse subsurface images using much reduced measurement by exploiting its sparsity. However, for landmine detection purposes, CS faces some challenges because the landmine is not exactly a point target and also faces high level clutter from the propagation in the medium. By exploiting the physical characteristics of the landmine using model-based CS, the probability of landmine detection can be increased. Using a small pixel size, the landmine reflection in the image is represented by several pixels grouped in a three dimensional plane. This block structure can be used in the model based CS processing for imaging the buried landmine. The evaluation using laboratory data and datasets obtained from an actual mine field in Cambodia shows that the model-based CS gives better reconstruction of landmine images than conventional CS.