With the increasing number of users, high spectral efficiency and low energy consumption requirements, the 5th generation (5G) communication system, which is the next generation communication system, is emerged. In this paper, we present a new multiuser detection method based on compressed sensing in the sparse code multiple access. Since compressed sensing (CS) is the theory of sparse signal recovery with small number of measurement samples, the proposed method consists two steps. In the first step, the initial detection is that the message passing algorithm (MPA) is used with several iterations, and in the second step, the sparse error correction in which the more accurate error vector is obtained. The proposed method uses the compressive sampling matching pursuit (CoSaMP) algorithm which is one of the greedy algorithms. The final estimated vector is obtained by combining vectors from these steps. The improved method provides better symbol-error rate (SER) performance with low complexity than the original MPA.