For inverse synthetic aperture radar imagery, the inherent sparsity of the scatterers in the range-Doppler domain has been exploited to achieve a high-resolution range profile or Doppler spectrum. Prior to applying the sparse recovery technique, preprocessing procedures are performed for the minimization of the translational-motion-induced Doppler effects. Due to the imperfection of coarse motion compensation, the autofocus technique is further required to eliminate the residual phase errors. This paper considers the phase error correction problem in the context of the sparse signal recovery technique. In order to encode sparsity, a multitask Bayesian model is utilized to probabilistically formulate this problem in a hierarchical manner. In this novel method, a focused high-resolution radar image is obtained by estimating the sparse scattering coefficients and phase errors in individual and global stages, respectively, to statistically make use of the sparsity. The superiority of this algorithm is that the uncertainty information of the estimation can be properly incorporated to obtain enhanced estimation accuracy. Moreover, the proposed algorithm achieves guaranteed convergence and avoids a tedious parameter-tuning procedure. Experimental results based on synthetic and practical data have demonstrated that our method has a desirable denoising capability and can produce a relatively well-focused image of the target, particularly in low signal-to-noise ratio and high undersampling ratio scenarios, compared with other recently reported methods.