Image deconvolution aims to recover an image that has been degraded by a linear operation such as blurring during image acquisition. Deconvolution based on maximum a-posteriori (MAP) estimation requires the global prior probability of the original image. Conventional methods usually model the image priors by uniformly characterizing the statistical properties of either some forward measurements of images or the representation coefficients in frames, neglecting the local image statistics. In this paper, we adopt local sparse representation in image deconvolution. Our contributions include proposing (1) a joint model of natural images combining sparse representation of image patches and sparse gradient priors, and (2) an efficient iterative algorithm to infer the MAP estimate of image deconvolution using the proposed model. Experiments indicate that the proposed method can recover the original image with high peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) index compared with state-of-the-art methods.