Unsupervised image-to-image translation aims to learn the mapping from an input image in a source domain to an output image in a target domain without paired training dataset. Recently, remarkable progress has been made in translation due to the development of generative adversarial networks (GANs). However, existing methods suffer from the training instability as gradients passing from discriminator to generator become less informative when the source and target domains exhibit sufficiently large discrepancies in appearance or shape. To handle this challenging problem, in this paper, we propose a novel multi-constraint adversarial model (MCGAN) for image translation in which multiple adversarial constraints are applied at generator's multi-scale outputs by a single discriminator to pass gradients to all the scales simultaneously and assist generator training for capturing large discrepancies in appearance between two domains. We further notice that the solution to regularize generator is helpful in stabilizing adversarial training, but results may have unreasonable structure or blurriness due to less context information flow from discriminator to generator. Therefore, we adopt dense combinations of the dilated convolutions at discriminator for supporting more information flow to generator. With extensive experiments on three public datasets, cat-to-dog, horse-to-zebra, and apple-to-orange, our method significantly improves state-of-the-arts on all datasets.