In intensity-modulation and direct-detection (IM/DD) multiple-input and multiple-output (MIMO) visible light communication (VLC) systems, spatial subchannels are usually correlated, and spatial modulation is a good choice to achieve the advantages of MIMO technology. Peak-to-average power ratio (PAPR) is a key issue in VLCs due to the limited linear dynamic range of light emitting diodes (LEDs). Single-carrier communication systems have a lower PAPR than orthogonal frequency division multiplexing (OFDM) communication systems. However, it is challenging to design a single-carrier spatial modulation for high-rate transmissions because of the time domain intersymbol interference. This paper develops an optical spatial modulation (OSM) scheme based on bipolar pulse amplitude modulation (PAM) and spatial elements for high-rate indoor VLC systems. Multiple data streams can be transmitted simultaneously in the proposed scheme. Based on the transmit strategy, we develop a low-complexity receiver algorithm that achieves better bit-error rate performance than reference schemes, and the proposed OSM scheme has a much lower PAPR than OFDM based OSM schemes. When the spatial subchannels are highly correlated, a spatial area division strategy is applied, and the receiver algorithm is investigated. The symbol-error rate expression of the proposed OSM scheme is derived, and the computational complexity is analyzed.