Despite generative adversarial networks (GANs) can hallucinate promising-quality high-resolution (HR) faces from low-resolution (LR) faces, they cannot guarantee preserving the identities of hallucinated HR faces, making the HR faces poorly recognizable. To address this problem, we propose a Siamese GAN (SiGAN) to reconstruct HR faces that visually resemble their corresponding identities. On top of a Siamese network, the proposed SiGAN consists of a pair of two identical generators and one discriminator. We incorporate reconstruction error and identity label information in the loss function of SiGAN in a pairwise manner. By iteratively optimizing the loss functions of the generator pair and discriminator of SiGAN, we not only achieve visually-pleasant face reconstruction, but also ensure that the reconstructed information is useful for identity recognition. Experimental results demonstrate that SiGAN significantly outperforms existing face hallucination GANs in objective face verification performance, while achieving promising visualquality reconstruction. Moreover, for input LR faces from unseen identities who are not included in training, SiGAN can still do a good job.