For downward-looking linear array 3-D synthetic aperture radar, the resolution in cross-track direction is much lower than the ones in range and azimuth. Hence, superresolution reconstruction algorithms are desired. Since the cross-track signal to be reconstructed is sparse in the object domain, compressive sensing algorithm has been used. However, the imaging processing on the 3-D scene brings large computational loads, which renders challenges in both data acquisition and processing. To cover this shortage, truncated singular value decomposition is utilized to reconstruct a reduced-redundancy spatial measurement matrix. The proposed algorithm provides advantages in terms of computational time while maintaining the quality of the scene reconstructions. Moreover, our results on uniform linear array are generally applicable to sparse nonuniform linear array. Superresolution properties and reconstruction accuracies are demonstrated using simulations under the noise and clutter scenarios.