In the field of drug discovery and development, deep learning techniques have become a powerful tool to accelerate the discovery and development of new drugs. In the design and optimization of lead molecules, generative adversarial network and graph neural network are one of the prime techniques for accelerating research and development, because the former is based on the idea of two-player game to learn drug features to generate effective molecules, while the unstructured inputs of the latter are well-suited for the analysis of molecular data. Therefore, this study develops a new graph generative adversarial model, called PreZ-DGGAN, by inserting the graph neural network layer into the generative adversarial network. Within PreZ-DGGAN, the latent variable input of the generator is pre-learned by an improved graph variational autoencoder, which effectively avoids the mode collapse of the generative adversarial network, whereas the hidden layer of the discriminator is graph neural network layer, which is able to better learn the real molecules and judge the generated molecules as true or false. Experiments on two molecule datasets show that the molecules generated by PreZ-DGGAN have higher validity (100% on average) and uniqueness (91.5% on average), and the generated molecules are more diverse in structure.