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Existing face swap methods rely heavily on large-scale networks for adequate capacity to generate visually plausible results, which inhibits its applications on resource-constraint platforms. In this work, we propose MobileFSGAN, a novel lightweight GAN for face swap that can run on mobile devices with much fewer parameters while achieving competitive performance. A lightweight encoder-decoder structure is designed especially for image synthesis tasks, which is only 10.2MB and can run on mobile devices at a real-time speed. To tackle the unstability of training such a small network, we construct the FSTriplets dataset utilizing facial attribute editing techniques. FSTriplets provides source-target-result training triplets, yielding pixel-level labels thus for the first time making the training process supervised. We also designed multi-scale gradient losses for efficient back-propagation, resulting in faster and better convergence. Experimental results show that our model reaches comparable performance towards state-of-the-art methods, while significantly reducing the number of network parameters. Codes and the dataset have been released.