Learning an autonomous dynamic system (ADS) encoding human motion rules has been shown as an effective way for human motion skills transfer. However, most existing approaches focus on goal-directed motion skills transfer, and the study on periodic motion skills transfer is rare. One popular approach for periodic motion skills transfer is learning periodic dynamic movement primitive (DMP); however, periodic DMP is sensitive to spatial disturbances due to the introduction of the phase parameters. To solve this issue, this brief presents a novel approach to learn an ADS with a stable limit cycle without introducing phase parameters. First, a data-driven Lyapunov function (energy function) is learned, such that one of its level surfaces is consistent with periodic human demonstration trajectories. Then, an ADS is learned by sequentially solving energy function-related constrained optimization problems. With a proper design of constraint functions, we can ensure that the trajectory generated by the ADS will converge to an energy function-level surface, of which the shape is similar to periodic human demonstration trajectories. Experiments are conducted to show the effectiveness of the proposed approach (PA).