In this paper, we propose a soft-decoding near-ML MIMO demodulation scheme that achieves near optimal performance with fixed and low complexity. Exploiting the regular structure of bit-to-symbol mapping, the proposed scheme performs hard demodulation to find the first candidate symbol for each stream followed by selection of nearby candidate points such that at least one candidate exists for the computation of likelihood information of bit 0 and 1 without intermediate calculation of the Euclidean distance. This demodulation scheme enables an improvement in performance by guaranteeing the existence of candidates and a significant reduction in the number of distance calculations which is a major complexity burden. The performance is evaluated by computer simulation, and computational complexity is also assessed in terms of the number of complex multiplication.