Although MIMO technology can improve the utilization rate of spectrum, multi-dimensional signal processing brings great challenges to the detection of MIMO signals. Based on the analysis of various MIMO detection algorithms, QR decomposition is selected as the research object, which is a kind of nonlinear algorithm. In order to obtain higher performance of detection, the sorted QR decomposition is further studied and propose the sorting scheme based on L1-norm. Using Matlab for performance simulation, the L1-norm sorting strategy and the L2-nrom sorting strategy have basically the same impact on MIMO system, but the L1-norm sorting strategy reduces the computational complexity. On this basis, the hardware structure of improved sorted QR decomposition by Givens rotation on FPGA is proposed. Comparing with the solution of L2-norm, the L1-norm strategy reduces at least 29.2% combinational logic resources and 32.4% register resources when calculating a single column norm in the realization of 4×4 channel matrix decomposition. Comparing with similar designs, the frequency of operating clock has been significantly improved.