The human face is one of the most interesting subjects involved in numerous applications. Significant progress has been made towards the image deblurring problem, however, existing generic deblurring methods are not able to achieve satisfying results on blurry face images. The success of the state-of-the-art image deblurring methods stems mainly from implicit or explicit restoration of salient edges for kernel estimation. When there is not much texture in the blurry image (e.g., face images), existing methods are less effective as only few edges can be used for kernel estimation. Moreover, recent methods are usually jeopardized by selecting ambiguous edges, which are imaged from the same edge of the object after blur, for kernel estimation due to local edge selection strategies. In this paper, we address these problems of deblurring face images by exploiting facial structures. We propose a maximum a posteriori (MAP) deblurring algorithm based on an exemplar dataset, without using the coarse-to-fine strategy or ad-hoc edge selections. Extensive evaluations against state-of-the-art methods demonstrate the effectiveness of the proposed algorithm for deblurring face images. We also show the extendability of our method to other specific deblurring tasks.