To solve the off grid problem in compressed sensing (CS) based inverse synthetic aperture radar (ISAR) imaging, a fast and accurate algorithm has been proposed in the paper. By jointly estimating the off grid error and the sparse solution, off grid ISAR imaging is transformed into a joint optimization problem. Interestingly, it can be solved efficiently through two least squares problems based on first order Taylor approximation. When applied to complex sinusoids and quasi real ISAR data, the proposed algorithm has got better results than the conventional algorithm. Therefore, it is a promising off grid CS based ISAR imaging algorithm.