Gaze estimation aims to accurately estimate the direction or position at which a person is looking. With the development of deep learning techniques, a number of gaze estimation methods have been proposed and achieved state-of-the-art performance. However, these methods are limited to within-dataset settings, whose performance drops when tested on unseen datasets. We argue that this is caused by infinite and continuous gaze labels. To alleviate this problem, we propose using gaze frontalization as an auxiliary task to constrain gaze estimation. Based on this, we propose a novel gaze domain generalization framework named Gaze Frontalization-based Auxiliary Learning (GFAL) Framework which embeds the gaze frontalization process, i.e., guiding the feature so that the eyeball can rotate and look at the front (camera), without any target domain information during training. Experimental results show that our proposed framework is able to achieve state-of-the-art performance on gaze domain generalization task, which is competitive with or even superior to the SOTA gaze unsupervised domain adaptation methods.