Recent generative adversarial networks (GANs) have yielded remarkable performance in face image synthesis. GAN inversion embeds an image into the latent space of a pretrained generator, enabling it to be used for real face manipulation. However, current inversion approaches for real faces suffer the dilemma of initialization collapse and identity loss. In this paper, we propose a hierarchical GAN inversion for real faces with identity preservation based on mutual information maximization. We first use a facial domain guaranteed initialization to avoid the initialization collapse. Furthermore, we prove that maximizing the mutual information between inverted faces and their identities is equivalent to minimizing the distance between identity features from inverted and original faces. Optimization for real face inversion with identity preservation is implemented on this mutual information-maximizing constraint. Extensive experimental results show that our approach outperforms state-of-the-art solutions for inverting and editing real faces, particularly in terms of face identity preservation.