To reduce interference from cognitive users with licensed users, and raise spectrum efficiency as much as possible in cognitive radio spectrum access based on fixed sensing period (FSP), a new technique called dynamic spectrum access using joint probability channel prediction (JPCP) based on hidden Markov model (HMM) is proposed. After cognitive users have occupied a licensed spectrum, whether it should quit the channel can be determined by comparing the JPCP value with the threshold defined to reduce interference from cognitive users with licensed users. When cognitive users fail to access the licensed spectrum, a temporary spectrum sensing mechanism is inserted to efficiently find the spectral slot in the licensed spectrum to raise efficiency of cognitive users. Simulation shows that, as compared to the conventional FSP, the proposed technique can reduce interference from cognitive users with licensed users, and raise spectrum efficiency of cognitive users.