Sparse aperture ISAR autofocusing and imaging is generally achieved by methods of compressive sensing (CS), or, sparse signal recovery, because non-uniform sampling of sparse aperture disables fast Fourier transform (FFT)-the core of traditional ISAR imaging algorithms. Note that the CS based ISAR autofocusing methods are often computationally heavy to execute, which limits their applications in real-time ISAR systems. The improvement of computational efficiency of sparse aperture ISAR autofocusing is either necessary or at least highly desirable to promote their practical usage. This paper proposes an efficient sparse aperture ISAR autofocusing algorithm. To eliminate the effect of sparse aperture, the ISAR image is reconstructed by sparse Bayesian learning (SBL), and the phase error is estimated by minimum entropy during the reconstruction of ISAR image. However, the computation of expectation in SBL involves a matrix inversion with an intolerable computational complexity of at least O(L3). Here, in the Bayesian inference of SBL, we transform the time-consuming matrix inversion into an element-wise matrix division by the alternating direction method of multipliers (ADMM). An auxiliary variable is introduced to divide the computation of posterior into three simpler subproblems, bringing computational efficiency improvement. Experimental results based on both simulated and measured data validate the effectiveness as well as high efficiency of the proposed algorithm. It is 20-30 times faster than the SBL based sparse aperture ISAR autofocusing approach.