The privacy and security of face data on social media are facing unprecedented challenges as it is vulnerable to unauthorized access and identification. A common practice for solving this problem is to modify the original data so that it could be protected from being recognized by malicious face recognition (FR) systems. However, such ``adversarial examples'' obtained by existing methods usually suffer from low transferability and poor image quality, which severely limits the application of these methods in real-world scenarios. In this paper, we propose a 3D-Aware Adversarial Makeup Generation GAN (3DAM-GAN). which aims to improve the quality and transferability of synthetic makeup for identity information concealing. Specifically, a UV-based generator consisting of a novel Makeup Adjustment Module (MAM) and Makeup Transfer Module (MTM) is designed to render realistic and robust makeup with the aid of symmetric characteristics of human faces. Moreover, a makeup attack mechanism with an ensemble training strategy is proposed to boost the transferability of black-box models. Extensive experiment results on several benchmark datasets demonstrate that 3DAM-GAN could effectively protect faces against various FR models, including both publicly available state-of-the-art models and commercial face verification APIs, such as Face++, Baidu and Aliyun.