Spatial modulation (SM) is a multiple-input multiple-output (MIMO) transmission technique that maps the information into both antenna indices and signals from a conventional signal constellation. Block Markov superposition transmission (BMST) is a recently proposed coding scheme which has a good performance and a predictable performance lower bound. In this letter, we propose to combine the BMST with the SM, resulting in a system, which is acronymized as BMST-SM for convenience. Also presented is a sliding-window decoding executed iteratively between the BMST decoder and the soft-in soft-out (SISO) SM demapper. To evaluate the performance of the BMST-SM system, the mutual information is derived for the SM with multiple receive antennas under uniformly distributed input constraint. Simulation results show that the BMST-SM scheme performs around one dB away from the Shannon limit at the bit-error-rate (BER) around 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> over uncorrelated Rayleigh fading channels.