Gaze estimation often requires a large scale datasets with well annotated gaze information to train the estimator. However, such a dataset requires costive annotation and is usually very difficult to collect. Therefore, a number of gaze redirection approaches have been proposed to address such a problem. However, existing methods lack the ability to precisely synthesize images with target gaze and head pose in complex lighting scenes. As a powerful technique to model the distribution of given data, normalizing flows have the ability to generate photo-realistic images and provide flexible latent space manipulation. In this work, we present a novel flow-based generative model, GazeFlow11The code will be made available at https://github.com/CVI-SZU/GazeFlow, for gaze redirection. The visual results of gaze redirection show that the quality of eye images synthesized by GazeFlow is significantly higher than that of other approaches like Deep Warp and PRGAN. Our approach has also been applied to augment the training data to improve the accuracy of gaze estimators and significant improvement has been achieved for both within dataset and cross dataset experiments.