Spectrum sensing is one of the most challenging problems in cognitive radio systems. It is frequently impractical to implement theoretical methods due to the limitation of the existing hardware operational bandwidth. To solve this problem, an emerging technique, compressive sensing (CS), is introduced to cognitive radio field so that only compressive measurements are needed in real implementation and the requirement for the hardware bandwidth is reduced. In this paper, a modified CS algorithm named Neighbor Orthogonal Matching Pursuit (NOMP) is proposed to detect the spectrum usage state in cognitive networks. It combines the continuous property of real-world spectrum and the Orthogonal Matching Pursuit(OMP) Method. Compared with the traditional CS algorithms such as matching pursuit (MP), OMP and Bayesian Compressive Sensing(BCS) methods, the modified algorithm can provide a reconstruction ability with much higher accuracy. Meanwhile, it is also a computational efficient method that costs less computation time than the other three methods under low SNR condition.