Based on the low imaging resolution of bistatic inverse synthetic aperture radar (Bi-ISAR) and the failure of pulse correlation under the condition of sparse aperture cause that of the traditional self-focusing algorithm, a Bi-ISAR sparse aperture self-focusing algorithm with the combined constraint of image quality optimization and sparsity is proposed. First, the proposed algorithm establishes the Bi-ISAR sparse aperture self-focusing signal model, reconstructs images through fast sparse Bayesian learning (FSBL), uses the minimum Tsallis entropy and constraints the reconstruction process, iteratively updates the phase error, and performs self-focusing to realize the initial phase correction of Bi-ISAR images. Simulation results show that the proposed algorithm has a fast convergence speed, strong robustness to noise, and high accuracy in reconstructing images.