Video style transfer techniques inspire many exciting applications on mobile devices. However, their efficiency and stability are still far from satisfactory. To boost the transfer stability across frames, optical flow is widely adopted, despite its high computational complexity, e.g. occupying over 97% inference time. This paper proposes to learn a lightweight video style transfer network via knowledge distillation paradigm. We adopt two teacher networks, one of which takes optical flow during inference while the other does not. The output difference between these two teacher networks highlights the improvements made by optical flow, which is then adopted to distill the target student network. Furthermore, a low-rank distillation loss is employed to stabilize the output of student network by mimicking the rank of input videos. Extensive experiments demonstrate that our student network without an optical flow module is still able to generate stable video and runs much faster than the teacher network.