Abstract: Compared with traditional spectrum sensing methods, compressed sensing based spectrum sensing can fast obtain a signal with a lower sampling rate and then use the obtained data to determine the channel occupancy. However, the reconstruction algorithm in compressed sensing techniques is usually too complex to meet the requirements of real-time communication. A prediction based differential signal compression sensing algorithm is proposed in this paper, which utilize time correlation of the channel to build a prediction model and predict the changes of channel occupancy. In following process of reconstruction, based on the prediction result, the search range of frequency points can been reduced, thus reducing the number of iterations of the reconstruction algorithm . Simulation results show that the new algorithm can significantly reduce computational complexity and ensure good sensing performance at the same time.