Sparse representation based classification (SRC) was originally applied to multiple-training-sample face recognition with promising performance. Recently SRC has been extended to face recognition with single sample per person by using variations extracted from a generic training set as an additional common dictionary. However, the extended SRC ignored to learn a better variation dictionary and to use local region information of face images. To address this issue, we propose a local variation joint representation (LVJR) method, which learns a variation dictionary and does joint and local collaborative representation for a query image. The learned variation dictionary was required to do similar representation for the same-type facial variations, while the joint and local collaborative representation could effectively use local information of face images. Experiments on the large-scale CMU Multi-PIE and AR databases demonstrate that the proposed LVJR method achieves better results compared with the existing solutions to the single sample per person problem.