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Spectrum sensing is one of the key issues in cognitive radio networks.Most of previous work concentrates on sensing the spectrum in a single spectrum band.In this paper,we propose a spectrum sensing sequence prediction scheme for cognitive radio networks with multiple spectrum bands to decrease the spectrum sensing time and increase the throughput of secondary users.The scheme is based on recent advances in computational learning theory,which has shown that prediction is synonymous with data compression.A Ziv-Lempel data compression algorithm is used to design our spectrum sensing sequence prediction scheme.The spectrum band usage history is used for the prediction in our proposed scheme.Simulation results show that the proposed scheme can reduce the average sensing time and improve the system throughput significantly.