Due to the poor spectrum utilization in time and space, the spectrum in cognitive radio is not only sparse but clusters in blocks in many situations. Based on the fact, a novel Bayesian compressed sensing algorithm for wideband spectrum sensing is proposed. In our proposed framework, firstly, the original signal should be sampled with sub-Nyquist sampling rate. Secondly, the clustering of the spectrum molded by many block structures is also utilized to increase the accuracy of spectrum sensing. Lastly, with a variational Bayesian inference, the experimental results show the validity and advantage of our proposed approach.