Abstract: Linear array synthetic aperture radar (LASAR) three-dimensional (3-D) imaging technology is a promising innovative 3-D radar imaging technology. As several antenna phase centers (APCs) activity in one pulse repetition time (PRT) simultaneously, it is very difficult to accurately compensate the motion errors of these APCs using navigation measurement data (e.g. inertial measuring unit and global positioning system) only. In this paper, a novel autofocus algorithm is proposed for LASAR 3-D imaging by exploiting maximum sharpness back projection via semidefinite programming. In the scheme, the linear mathematical model of back projection algorithm processing is set up, an iterative method aiming to maximize the LASAR image sharpness is derived to obtain the motion errors of the APCs. Moreover, to improve computational efficacy, only the dominant scatterers are selected as the input of the phase-error estimation. The effectiveness of the algorithm is demonstrated with both simulation and experimental examples.