Lattice-reduction (LR) technique has been adopted to improve the performance and reduce the complexity in MIMO data detection. This paper presents an improved quantization scheme for LR aided MIMO detection based on Gram-Schmidt orthogonalization. For the LR aided detection, the quantization step applies the simple rounding operation, which often leads to the quantization errors. Meanwhile, these errors may result in the detection errors. Hence the purpose of the proposed detection is to further solve the problem of degrading the performance due to the quantization errors in the signal estimation. In this paper, the proposed quantization scheme decreases the quantization errors using a simple tree search with a threshold function. Through the analysis and the simulation results, we observe that the proposed detection can achieve the nearly optimal performance with very low complexity, and require a little additional complexity compared to the conventional LR-MMSE detection in the high E_b/N₀ region. Furthermore, this quantization error reduction scheme is also efficient even for the high modulation order.