A decreasing candidate set regularized subspace pursuit algorithm is proposed to improve the signal reconstruction probability and precision of the subspace pursuit algorithm in compressed sensing. The proposed algorithm is improved based on the CoSaMP/SP algorithm, which divides the iterative process into several stages. Similar CoSaMP/SP algorithm is adopted to iterative calculation during each of the stages. The number of candidate set atoms is successively decreasing in each stage, and the new candidate set atoms are selected by using the regularization method. Compared to other algorithms, the simulation results show that the proposed algorithm can reconstruct the signal with higher probability and has high reconstruction precision in the noise environment.