Abstract-We propose a maximum likelihood block signal detection using QR decomposition and M-algorithm (called QRM-MLBD) for training sequence-aided single-carrier (TA-SC) multi-input multi-output (MIMO) spatial multiplexing. QRM-MLBD can significantly improve the packet error rate (PER) performance of cyclic prefix-inserted single-carrier (CP-SC) MIMO spatial multiplexing when compared to the frequency-domain minimum mean square error (MMSE) detection. However, in order to achieve the sufficiently improved performance, the use of a fairly large number M of surviving paths in the M-algorithm is required because if smaller M is used, the probability of removing the correct path at early stages increases. In this paper, to reduce this probability, we propose the use of TA-SC transmission instead of CP-SC transmission and show that the use of training sequence can significantly reduce the probability of removing the correct path at early stages in QRM-MLBD. We show, by computer simulation, that TA-SC MIMO spatial multiplexing using QRM-MLBD can achieve the PER performance similar to CP-SC MIMO spatial multiplexing while significantly reducing the computational complexity, about 8% of computational complexity of CP-SC MIMO in the case of 16QAM and 4×4 MIMO spatial multiplexing.