To relieve the impact caused by different arrival times of multiple users in the uplink MIMO-SCMA system, a grouped multiuser transmission model, according to different delays and its corresponding detection scheme, is proposed in this paper. Assuming perfect synchronization in one group, a message-passing algorithm based on serial propagation (SP-MPA) is proposed to reduce the bit error rate (BER), which could transfer the updated information to the next symbol as its initial probability. Furthermore, with a more practical case, the partial Gaussian approximation method (PGA) is designed to decrease the interference resulting from the imperfect synchronization in one group. As the result, the computing complexity of the proposed PGA method could be decreased by at least 20% compared with SP-MPA and the BER could be improved by about 10%.