The computational prediction of novel drug-target interactions (DTIs) may effectively speed up the process of drug repositioning and reduce its costs. Most previous methods integrated multiple kinds of connections about drugs and targets by constructing shallow prediction models. These methods failed to deeply learn the low-dimension feature vectors for drugs and targets and ignored the distribution of these feature vectors. We proposed a graph convolutional autoencoder and generative adversarial network (GAN)-based method, GANDTI, to predict DTIs. We constructed a drug-target heterogeneous network to integrate various connections related to drugs and targets, i.e., the similarities and interactions between drugs or between targets and the interactions between drugs and targets. A graph convolutional autoencoder was established to learn the network embeddings of the drug and target nodes in a low-dimensional feature space, and the autoencoder deeply integrated different kinds of connections within the network. A GAN was introduced to regularize the feature vectors of nodes into a Gaussian distribution. Severe class imbalance exists between known and unknown DTIs. Thus, we constructed a classifier based on an ensemble learning model, LightGBM, to estimate the interaction propensities of drugs and targets. This classifier completely exploited all unknown DTIs and counteracted the negative effect of class imbalance. The experimental results indicated that GANDTI outperforms several state-of-the-art methods for DTI prediction. Additionally, case studies of five drugs demonstrated the ability of GANDTI to discover the potential targets for drugs.