Face sketch synthesis is a crucial issue in digital entertainment and law enforcement. It can bridge the considerable texture discrepancy between face photos and sketches. Most of the current face sketch synthesis approaches directly to learn the relationship between the photos and sketches, and it is very difficult for them to generate the individual specific features, which we call rare characteristics. In this paper, we propose a novel face sketch synthesis approach through residual learning. In contrast to traditional approaches, which aim to reconstruct a sketch image directly (i.e., learn the mapping relationship between the photo and sketch), we aim to predict the residual image by learning the mapping relationship between the photo and residual, i.e., the difference between the photo and sketch, given an observed photo. This technique will render optimizing the residual mapping easier than optimizing the original mapping and deriving rare characteristic information. We also introduce a joint dictionary learning algorithm by preserving the local geometry structure of a data space. Through the learned joint dictionary, we transform the face sketch synthesis from an image space to a new and compact space; the new and compact space is spanned by learned dictionary atoms, where the manifold assumption can be further guaranteed. Results show that the proposed method demonstrates an impressive performance in the face sketch synthesis task on three public face sketch datasets and various real-world photos. These results are derived by comparing the proposed method with several state-of-the-art techniques, including certain recently proposed deep learning-based approaches.