In a periodic spectrum sensing framework where each frame consists of a sensing block and a data transmitting block, increasing sensing duration decreases the probabilities of both missed opportunity and interference with primary users, but increasing sensing duration also decreases the energy efficiency and the transmitting efficiency of the cognitive network. Therefore, the sensing duration to use is a trade-off between sensing performance and system efficiencies. The relationships between sensing duration and state transition probability are analyzed firstly, when the licensed channel stays in the idle and busy states respectively. Then a state transition probability based sensing duration optimization algorithm is proposed, which can dynamically optimize the sensing duration of each frame in the current idle/busy state by predicting each frame's state transition probability at the beginning of the current state. Analysis and simulation results reveal that the time-varying optimal sensing duration increases as the state transition probability increases and compared to the existing method, the proposed algorithm can use as little sensing duration in each frame as possible to satisfy the sensing performance constraints so as to maximize the energy and transmitting efficiencies of the cognitive networks.