A novel rate splitting space division multiple access (SDMA) scheme based on grouped code index modulation (GrCIM) is proposed for the sixth generation (6G) downlink transmission. The proposed RSMA-GrCIM scheme transmits information to multiple user equipments (UEs) through the space division multiple access (SDMA) technique, and exploits code index modulation for rate splitting. Since the CIM scheme conveys information bits via the index of the selected Walsh code and binary phase shift keying (BPSK) signal, our RSMA scheme transmits the private messages of each user through the indices, and the common messages via the BPSK signal. Moreover, the Walsh code set is grouped into several orthogonal subsets to eliminate the interference from other users. A maximum likelihood (ML) detector is used to recovery the source bits, and a mathematical analysis is provided for the upper bound bit error ratio (BER) of each user. Comparisons are also made between our proposed scheme and the traditional SDMA scheme in spectrum utilization, number of available UEs, etc. Numerical results are given to verify the effectiveness of the proposed SDMA-GrCIM scheme.