Video style transfer is a useful component for applications such as augmented reality, non-photorealistic rendering, and interactive games. Many existing methods use optical flow to preserve the temporal smoothness of the synthesized video. However, the estimation of optical flow is sensitive to occlusions and rapid motions. Thus, in this work, we introduce a novel evolve-sync loss computed by evolvements to replace optical flow. Using this evolve-sync loss, we build an adversarial learning framework, termed as Video Style Transfer Generative Adversarial Network (VST-GAN), which improves upon the MGAN method for image style transfer for more efficient video style transfer. We perform extensive experimental evaluations of our method and show quantitative and qualitative improvements over the state-of-the-art methods.