Recent years have witnessed the dramatically increased interest in face generation with generative adversarial networks (GANs). A number of successful GAN algorithms have been developed to produce vivid face images towards different application scenarios. However, little work has been dedicated to automatic quality assessment of such GAN-generated face images (GFIs), even less have been devoted to generalized and robust quality assessment of GFIs generated with unseen GAN model. Herein, we make the first attempt to study the subjective and objective quality towards generalized quality assessment of GFIs. More specifically, we establish a large-scale database consisting of GFIs from four GAN algorithms, the pseudo labels from image quality assessment (IQA) measures, as well as the human opinion scores via subjective testing. Subsequently, we develop a quality assessment model that is able to deliver accurate quality predictions for GFIs from both available and unseen GAN algorithms based on meta-learning. In particular, to learn shared knowledge from GFIs pairs that are born of limited GAN algorithms, we develop the convolutional block attention (CBA) and facial attributes-based analysis (ABA) modules, ensuring that the learned knowledge tends to be consistent with human visual perception. Extensive experiments exhibit that the proposed model achieves better performance compared with the state-of-the-art IQA models, and is capable of retaining the effectiveness when evaluating GFIs from the unseen GAN algorithms.