It is well-known that GANs are difficult to train, and several different techniques have been proposed in order to stabilize their training. In this paper, we propose a novel training method called manifold-matching, and a new GAN model called manifold-matching GAN (MMGAN). MMGAN finds two manifolds representing the vector representations of real and fake images. If these two manifolds match, it means that real and fake images are statistically identical. To assist the manifold-matching task, we also use i) kernel tricks to find better manifold structures, ii) moving-averaged manifolds across mini-batches, and iii) a regularizer based on correlation matrix to suppress mode collapse. We conduct in-depth experiments with three image datasets and compare with several state-of-the-art GAN models. 32.4% of images generated by the proposed MMGAN are recognized as fake images during our user study (16% enhancement compared to other state-of-the-art model). MMGAN achieved an unsupervised inception score of 7.8 for CIFAR-10.