The synergistic amalgamation of sparse code multiple access (SCMA) and multiple-input multiple-output (MIMO) technologies can be exploited for improving spectral efficiency and providing enhanced wireless services to massive users. In this case, however, channel estimation is a burning issue with the increasing number of users and/or antennas. To tackle this problem, we propose a novel non-coherent transmission scheme for SCMA, referred to as NC-SCMA. In the proposed NC-SCMA, each user first maps its binary data to sparse codewords, and then perform differential modulation on the non-zero dimensions. Upon receiving all users’ signals, we leverage the channel hardening effect to carry out differential demodulation and multi-user detection without any instantaneous channel state information. In addition, the design of the sparse codebooks in the NC-SCMA system is investigated with the aid of the pair-wise probability. Numerical results demonstrate the superiority of the proposed technique over the benchmark scheme in terms of bit error rate performance.