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A layered space-time trellis coded MIMO system (LST-MIMO) is studied to achieve very high-speed wireless data transmission. A minimum mean square error based successive interference cancellation receiver (MMSE-SIC) is proposed to obtain higher diversity gain in the space-time decoding process, which can dramatically improve the system performance. Given the channel state information (CSI), an ordering scheme is further proposed to optimize the decoding order, which can effectively suppress the error propagation and enhance the system reliability. The proposed MMSE-SIC receiver with the ordering scheme is also studied in a multipath propagation channel with wideband orthogonal frequency division multiplexing (OFDM). Simulation results demonstrate that the proposed ordered MMSE-SIC receiver can substantially outperform the conventional decoding algorithms, and therefore make LST-MIMO system a promising and efficient technique for future high-speed and high-rate data transmission in wireless communication systems.