Since it is difficult to collect face images of the same subject over a long range of age span, most existing face aging methods resort to unpaired datasets to learn age mappings. However, the matching ambiguity between young and aged face images inherent to unpaired training data may lead to unnatural changes of facial attributes during the aging process, which could not be solved by only enforcing identity consistency like most existing studies do. In this paper, we propose an attribute-aware face aging model with wavelet based Generative Adversarial Networks (GANs) to address the above issues. To be specific, we embed facial attribute vectors into both the generator and discriminator of the model to encourage each synthesized elderly face image to be faithful to the attribute of its corresponding input. In addition, a wavelet packet transform (WPT) module is incorporated to improve the visual fidelity of generated images by capturing age-related texture details at multiple scales in the frequency space. Qualitative results demonstrate the ability of our model in synthesizing visually plausible face images, and extensive quantitative evaluation results show that the proposed method achieves state-of-the-art performance on existing datasets.