To bring digital avatars into people’s lives, it is highly demanded to efficiently generate complete, realistic, and animatable head avatars. This task is challenging, and it is difficult for existing methods to satisfy all the requirements at once. To achieve these goals, we propose GANHead (Generative Animatable Neural Head Avatar), a novel generative head model that takes advantages of both the fine-grained control over the explicit expression parameters and the realistic rendering results of implicit representations. Specifically, GANHead represents coarse geometry, fine-gained details and texture via three networks in canonical space to obtain the ability to generate complete and realistic head avatars. To achieve flexible animation, we define the deformation filed by standard linear blend skinning (LBS), with the learned continuous pose and expression bases and LBS weights. This allows the avatars to be directly animated by FLAME parameters and generalize well to unseen poses and expressions. Compared to state-of-the-art (SOTA) methods, GANHead achieves superior performance on head avatar generation and raw scan fitting.