Single sample face recognition (FR) uses only one image per person for training. It is a challenging task due to insufficient training samples and dramatic variance of unseen images in real applications. In this paper, we propose a cycle-autoencoder model to generate facial variation from the single training sample and remove the variation in the testing set. Our approach adopts a cycle consistency scheme to formulate the generation and removal models in one framework. Considering the prior structure of the images produced from the generation and removal models, we further propose a block-sparse joint representation method, which integrates the representation procedure of all testing samples and obtains all the coefficients simultaneously. The experimental results on AR, Extended Yale B and CUFS datasets not only demonstrate the effectiveness of our proposed method, but also represent its robustness to complex facial variations. Experiments on the CUFS dataset also show that our approach is appropriate for sketch face recognition with single sample per person.