Imaging radar with a suboptimal aperture length usually has a poor azimuth resolution due to the limited aperture length and sparse non-uniform linear array configuration. To address this problem, an imaging algorithm combining pseudo-polar formatting and gridless sparse recovery method is proposed. After pseudo-polar formatting the echo signal, reweighted atomic norm minimisation is implemented for azimuth imaging to achieve performance with improved resolution and free of off-grid effect. Experiments on ground-based synthetic aperture radar verify the performance of the proposed algorithm.