We propose an imaging algorithm for downward-looking sparse linear array three-dimensional synthetic aperture radar (DLSLA 3-D SAR) in the circumstance of cross-track sparse and nonuniform array configuration. Considering the off-grid effect and the resolution improvement, the algorithm combines pseudo-polar formatting algorithm, reweighed atomic norm minimization (RANM), and a parametric relaxation-based cyclic approach (RELAX) to improve the imaging performance with a reduced number of array antennas. RANM is employed in the cross-track imaging after pseudo-polar formatting the DLSLA 3-D SAR echo signal, then the reconstructed results are refined by RELAX. By taking advantage of the reweighted scheme, RANM can improve the resolution of the atomic norm minimization, and outperforms discretized compressive sensing schemes that suffer from off-grid effect. The simulated and real data experiments of DLSLA 3-D SAR verify the performance of the proposed algorithm.