For sparse aperture (SA) radar imaging, the phase errors are difficult to be estimated, which challenges the traditional autofocusing for inverse synthetic aperture radar (ISAR) imaging. A novel Bayesian ISAR autofocusing algorithm for SA is proposed. We unfold the sparse Laplace prior to two layers so that the full variational Bayesian inference can be derived. To further exploit the prior knowledge on the structure of radar images, dependencies among adjacent pixels are considered to design a structured sparse prior. In addition, the minimum entropy criterion is utilized to estimate the phase error during the reconstruction of the ISAR image to achieve ISAR autofocusing. The superiority of the proposed method against the traditional sparsity-driven method is validated by the experimental results based on both simulated and measured data.