Estimation of channel capacity plays a crucial role in analyzing the performance of spatial modulation (SM) systems. So far, no analytic form of expression has been derived for SM systems with more than two transmit antennas. In this paper, the analytic form of expression is derived for computing the channel capacity using the Huffman mapping scheme for an adaptive SM system with four transmit antennas. Gauss hypergeometric function is exploited to derive the analytic form of expression for a 4×1 system. Analytical results show the validation of the derived expression.