Deep generative models for graphs have recently achieved great successes in modeling and generating graphs for studying networks in biology, engineering, and social sciences. However, they are typically unconditioned generative models that have no control over the target graphs given a source graph. In this article, we propose a novel graph-translation-generative-adversarial-nets (GT-GAN) model that transforms the source graphs into their target output graphs. GT-GAN consists of a graph translator equipped with innovative graph convolution and deconvolution layers to learn the translation mapping considering both global and local features. A new conditional graph discriminator is proposed to classify the target graphs by conditioning on source graphs while training. Extensive experiments on multiple synthetic and real-world datasets in the domain of cybernetworks, the Internet of Things, and neuroscience demonstrate that the proposed GT-GAN model significantly outperforms other baseline methods in terms of both effectiveness and scalability. For instance, GT-GAN outperforms the classical state-of-the-art (SOTA) methods in functional connectivity (FC) prediction of brain networks by at least 32.5%.