The compressed sensing theory was applied to curvilinear aperture optimizing and 3-dimentional target feature extraction of curvilinear synthetic aperture radar. First, the echo signal target sparse representation model was built. Based on the incoherence principle between sparse matrix and sampling matrix of the compressed sensing theory, a guideline of evaluation to curvilinear aperture optimizing was found. Moreover, the 3-dimentional target feature extraction was realized by employing the basis pursuit method. Simulation results prove the correctness of the aperture optimization strategies with the incoherence principle as well as the efficiency of the basis pursuit method in target feature extraction.