Linear Array Synthetic Aperture Radar (LASAR) is a novel and promising radar imaging technique. It is difficult to achieve high-resolution LASAR three-dimensional (3D) imaging using the traditional imaging methods based on match filter, because of limitations by the sizes of the linear array antenna and the platform. In this paper, by exploiting the prior distribution of the LASAR echoes and the observed scene, an LASAR high-resolution 3D algorithm based on sparse Bayesian regularization is proposed. The algorithm first combines the Bayesian principle and maximum likelihood estimation theory, and then a sparse Bayesian minimum cost function is constructed for LASAR target recovery. Second, using an iterative regularization reconstruction method, high-resolution imaging of LASAR sparse targets is achieved by solving a joint-norms optimization problem. In addition, for the problem of a large amount of sparse Bayesian regularization imaging, combined with the position prediction fast imaging idea, the threshold segmentation algorithm is used to extract the strong target of sparse coarse imaging, and then the algorithm operation efficiency is improved. Simulation and experiment results are presented to confirm the effectiveness of the algorithm.