Domain mismatch is a common problem in speaker verification. This paper proposes an information-maximized variational domain adversarial neural network (InfoVDANN) to reduce domain mismatch by incorporating an InfoVAE into domain adversarial training (DAT). DAT aims to produce speaker discriminative and domain-invariant features. The InfoVAE has two roles. First, it performs variational regularization on the learned features so that they follow a Gaussian distribution, which is essential for the standard PLDA backend. Second, it preserves mutual information between the features and the training set to extract extra speaker discriminative information. Experiments on both SRE16 and SRE18-CMN2 show that the InfoVDANN outperforms the recent VDANN, which suggests that increasing the mutual information between the latent features and input features enables the InfoVDANN to extract extra speaker information that is otherwise not possible.