At present, most of the sparse space-time adaptive processing(STAP) methods focus on exploiting the clutter sparsity. In this paper, different from the present sparse STAP methods, both the clutter sparsity and the target sparsity in STAP are considered at the same time, and a novel joint sparse STAP method is proposed. The proposed method imposes a sparse regularization on the clutter and the target to the minimum Capon Spectrum criterion. The processing results of the measured data shows that the output SCNR of the proposed method is 3dB higher than the method in [20] and 2dB higher than the method in [21].