In this paper, compressed sensing (CS) based new multiuser detector for sparse code multiple access (SCMA) systems is proposed. Since CS is the theory of sparse signal reconstruction with fewer samples, the proposed method consists of two steps. Firstly, in the initial detection, message passing algorithm (MPA) with several iterations is used. Then, based on the initial detection, the sparse error correction is applied to obtain the error vector more accurately. At this step, compressive sampling matching pursuit (CoSaMP) algorithm, which is one of the greedy algorithms, is used for sparse error correction. The final estimated vector is obtained from combining two vectors from these two steps. The developed method provides better symbol-error ratio (SER) performance with less iteration and less complexity than the original MPA.