In order to enable secondary or unlicensed users to obtain idle subbands on a given broadband for use, the broadband spectrum sensing technology in cognitive radio is discussed and an effective broadband spectrum sensing algorithm is proposed. The algorithm first uses Hidden Markov Model(HMM) to model the dynamic behavior of primary users to overcome the limitations of current broadband sensing technologies. Secondly, the proposed algorithm uses the existing narrowband sensing technology to divide the sensing spectrum band into smaller channels and model it as a balanced binary tree; then the spectrum holes are recursively searched. If any holes are detected to be adjacent in frequency, they are merged into a single spectrum hole for maximizing the capacity of cognitive secondary users over the entire frequency band. The simulation results show that compared with the existing broadband spectrum sensing methods, the proposed broadband spectrum sensing algorithm has better sensing performance gain and stronger robustness.