To support multiple users in an indoor multiple-input multiple-output visible light communication (MIMO-VLC) system adopting spatial multiplexing, orthogonal frequency division multiple access (OFDMA) is usually adopted, where the overall modulation bandwidth is shared by all the users. In this paper, by fully exploiting the spatial distributions of light-emitting diode (LED) transmitters in the ceiling and end users around the receiving plane, we propose a space division multiple access (SDMA) technique for indoor spatial multiplexing-based MIMO-VLC systems. When applying SDMA, users within the MIMO-VLC system are divided into different user groups (UGs) based on their spatial locations with respect to different LED transmitters. Specifically, each UG can use the overall modulation bandwidth of the system. For efficient implementation of SDMA, two distributed user grouping (DUG) approaches are proposed, including basic DUG and transmit diversity-enhanced DUG (TD-DUG), and a two-step resource allocation algorithm is further designed. The achievable rates of the MIMO-VLC system employing SDMA with both basic DUG and TD-DUG are derived accordingly. To verify the superiority of SDMA over conventional OFDMA, detailed analytical and simulation results are presented. Moreover, a proof-of-concept experiment is conducted to demonstrate the advantage of SDMA in a practical spatial multiplexing-based MIMO-VLC system. Index Terms-Distributed user grouping (DUG), multiple-input multiple-output (MIMO), space division multiple access (SDMA), visible light communication (VLC).