In this study we propose a hybrid spectrum sharing scheme based on power control by combining Overlay with Underlay schemes, to improve radio spectrum efficiency. In the scheme, the secondary users dynamically switch their operational states between Overlay and Underlay according to the spectrum occupancy. Thus the dynamics of the primary network is first modeled with a discrete-state Markov process to find the time fraction of secondary users in the Overlay state and that in the Underlay state, which leads to the capacity model of the hybrid spectrum sharing system. Under the criterion of maximizing capacity, the power allocation of the cognitive network is researched and the optimum power allocation for secondary users is deduced. As a result, the maximum achievable capacity of the cognitive network is obtained. Simulations are given to prove the analysis further. Theoretical and simulated results indicate that hybrid spectrum sharing based on power control provides a higher capacity than single Overlay and Underlay systems for the cognitive network, i.e., hybrid spectrum sharing can further improve radio spectrum efficiency.