Tomographic synthetic aperture radar (TomoSAR), which can provide 3-D image of the observed scenes, has become an important technology for topographic mapping, forest parameter estimation, urban buildings modeling, and so on. Recently, the developed compressed sensing (CS) and other similar methods have been widely applied for the achievement of super-resolution SAR tomography. However, there always exists inevitable model errors during the mining of scene information, such as discrete gridding on used dictionary and outliers among independent identically distribution (IID) samples, which tends to dramatically degrade the TomoSAR inversion. In this article, a novel robust gridless CS (RGLCS) algorithm is proposed for high-resolution 3-D imaging of array TomoSAR. In the scheme, the atomic norm minimization (ANM) is used to model the joint-sparsity (JS) pattern on elevation distribution between adjacent pixels, which can be treated as gridless CS to avoid the discrete error of the dictionary. Meanwhile, the outliers and disturbances not satisfying the IID elevation distribution are modeled as sparsely distributed spike noise in the image domain. The proposed RGLCS algorithm has the capability of perfectly separating the outliers and maintaining high-precision height resolution. For efficient solution, a fast alternative optimization is used to solve the objective function to effectively reduce the computational complexity. Next, the postprocessing, including point cloud clustering and double-bounce scattering detection and eliminating, are studied to obtain high-resolution 3-D point cloud image. Finally, the experimental analysis using both simulated and measured data is performed to verify the effectiveness of the proposed algorithm. In particular, a practical demonstration using measured airborne array TomoSAR data is presented for urban mapping.