In this paper, a partial sphere decoding approach is proposed to reduce the computational complexity of implementing the iterative MAP receiver for spatial multiplexing system, in which the complexity prohibitively increases with the number of transmit antennas and modulation order. The proposed approach considers only a subset of symbols with high a priori probabilities, i.e., more reliable ones, which allows for reducing the dimension of detection space. We design a novel reliability estimator which is used for dividing two subvectors according to reliability of individual symbol in the initial stage. Furthermore, a cost function-based partial MAP rule is applied to those subvectors so as to correct the initial estimation error in the course of iterative detection and decoding process. We have shown that the overall complexity of sphere decoding can be reduced by almost order of 2 in terms of floating point operations while maintaining the BER performance as close as 0.7dB to the conventional approach.