This paper proposes a hybrid cognitive radio (CR) system where underlay and overlay CR approaches are combined. Occasional switches from an overlay CR mode to an underlay CR mode enable to maximize the average throughput of a secondary (unlicensed) network and stable transmission of a secondary user. By controlling switching from an overlay CR mode to an underlay CR mode in a probabilistic sense, the throughput of a secondary user is maximized while the target departure rate of a primary (licensed) user is retained. Since a primary user in a hybrid approach is likely to suffer from additional interference, optimal transmit power of a secondary user in an overlay mode is derived for given switching rate. Our analysis and numerical results show that the proposed hybrid CR system takes benefits in maximizing throughput and maintaining stability of a queue.