Abstract: Wideband dynamic spectrum access based on cognitive radio has encountered bottleneck in the required speed of traditional sampling techniques. Compressive sensing (CS) emerged as an alternative candidate for wideband spectrum sensing at sub-Nyquist Sampling rates. Furthermore, exploiting and incorporating the prior information of related signals will signi?cantly reduce the sampling rate required by CS. Considering the sub-channel locations are known in advance, this paper proposes a new greedy algorithm, called Group-sparsity Orthogonal Matching Pursuit (GOMP), to reconstruct the wideband spectrum estimation by exploiting the characteristic of group sparsity corresponding to the channel distribution. The proposed algorithm based on the principle of the sophisticated greedy algorithm Orthogonal Matching Pursuit (OMP) incorporates a multipoint measurement of sub-channels to identify the signal support where active primary users are located. The multipoint measurement strategy converts the components of sub-channels into a L2-regularization, and then introduces the statistical characteristic of the regularization to identify the active sub-channels. This endows the algorithm with accuracy and robustness for signal support identification and spectrum reconstruction. A comparison experiment shows the proposed algorithm outperforms traditional OMP algorithm and the famous Basis Pursuit (BP) algorithm in terms of reconstruction errors and detection accuracy with fewer measurements. Moreover, it is faster than the two previous algorithms.