A new sidelobe-suppression algorithm was proposed for the synthetic aperture ladar(SAL) with high sidelobe data. The theory of compressed sensing (CS) indicates that the sidelobe of the sparse signal can be lowered while reconstructing the signal, but the image signal of SAL is not sparse. Therefore, a sidelobe suppressing algorithm based on the modified spatial variant apodization (SVA) and SAL image reconstructed by the CS was proposed to deal with the high-sidelobe problem in real-time data imaging. SAL image signal would be converted to be sparse by the modified SVA first and the sparse signal would be reconstructed by the CS. The sidelobe of the SAL simulation data and the real high-sidelobe SAL image data were all suppressed respectively. The simulation result shows that in the premise of no broadening mainlobe, the sidelobe of the SAL image signal can be effectively suppressed by this algorithm.