In Cognitive Radio Networks (CRNs), secondary users (unlicensed users) can use spectrum when their transmissions cause no interference to primary users (licensed users). The spectrum sensing is a necessity to achieve this spectrum sharing scheme. However, it is challenging to achieve spectrum sensing due to the computational complexity. In this paper, we propose a novel greedy algorithm to solve the wideband spectrum compressive sensing problem. The main idea of our algorithm is to reconstruct spectrum for wideband signals without any prior knowledge of spectrum. The proposed greedy algorithm will reconstruct wideband spectrum along with sub-bands of frequency in which spectrum is divided. The proposed greedy algorithm is intelligent enough to sense the range of each sub-band of frequency and detect them efficiently. Extensive simulation results show that our proposed algorithm outperforms existing greedy algorithms such as Orthogonal Matching Pursuit (OMP) in terms of accuracy, computational speed and Block OMP in terms of computational speed.