In this paper, we propose one grouped-iterative framework to generate a family of the MIMO detection algorithms. The presented framework not only includes the conventional iterative, grouped, and Chase detection algorithms, but also derives a new low-complexity MIMO detection algorithm. The proposed detection can adjust some parameters to achieve a range of trade-offs between performance and complexity. In (4,4) system with uncoded 16-QAM inputs, one instance of the proposed detection algorithm not only substantially reduces the multiplication complexity by 26.3% but also outperforms the BODF algorithm about 5dB. Another instance of the proposed algorithm can save multiplication complexity by 34% at the penalty of 1 dB loss compared with the B-Chase detector.