For cooperative cognitive radio networks (CR-Nets), spectrum sensing is a key technology to detect spectrum holes which are inadequacy exploited by primary communication system. This paper presents a novel compressed spectrum sensing method based on the structure prior information of the primary user signal for cooperative CR-Nets. In the proposed method, fusion central (FC) recombines the measurements sent by different CRs into a matrix which has block joint sparse structure. Exploiting this structure feature, a Block Stagewise Orthogonal Matching Pursuit (BStOMP) based on multiple measurement vector algorithm is proposed to quickly and effectively detect the active statuses of primary users (PUs). Simulations show that compared with the previous works, the proposed method has lower computation complexity and reliable recovery performance.