In recent years, Compressed Sensing (CS) has been a hot research topic. It has a wide range of applications, such as image processing and speech signal processing owing to its characteristic of removing redundant information by reducing the sampling rate. The disadvantage of CS is that the number of iterations in a greedy algorithm such as Orthogonal Matching Pursuit (OMP) is fixed, thus limiting reconstruction precision. Therefore, in this study, we present a novel Reducing Iteration Orthogonal Matching Pursuit (RIOMP) algorithm that calculates the correlation of the residual value and measurement matrix to reduce the number of iterations. The conditions for successful signal reconstruction are derived on the basis of detailed mathematical analyses. When compared with the OMP algorithm, the RIOMP algorithm has a smaller reconstruction error. Moreover, the proposed algorithm can accurately reconstruct signals in a shorter running time.