With the increasing wind power integration, the security and economy of the power system operations are greatly influenced by the intermittency and fluctuation of wind power. Due to the flexible operational modes for charging/discharging, the hybrid energy storage system (HESS) is composed of battery energy storage system and super-capacitor can effectively mitigate the wind power uncertainty. This paper proposes a probabilistic forecasting-based HESS sizing and control scheme to cost-effectively smooth wind power fluctuations. First, probabilistic wind power forecasting is combined with multivariate Gaussian copula to generate temporally correlated wind power scenarios. Then, an adaptive variational mode decomposition (VMD) method is proposed to extract the frequency components of each wind scenario and determine the pre-scheduled power of wind-HESS system adaptively. Finally, a two-stage stochastic optimization model is constructed to determine the capacity and correct the pre-scheduled power of HESS with the objective of minimizing total cost. Case studies based on actual data from a Danish wind farm demonstrate that the proposed HESS sizing and control scheme can significantly reduce the installation cost and operation cost of HESS and prominently smooth wind power fluctuations.