In wideband cognitive radio (CR) networks, high sampling rate, wireless fading channels and limitedhardware resources all impact the spectrum sensing. In this paper, a distributed compressive spectrum sensing algo-rithm based on the iterative support detection is proposed, in which CRs spread their detection information in thewhole network through the one-hop communication and the global consensus is achieved on the support set. Then,through a shared support set, the joint sparsity is utilized by CRs during the local sparse signal reconstruction, thusrealizing more accurate spectrum detection. Simulation results show that the proposed algorithm helps to achieveeffective spectrum detection at a sub-Nyquist sampling rate and possesses near-optimal detection performance in theabsence of a fusion center.