In this paper, we propose a new column swapping traverse Lenstra-Lenstra-Lovasz algorithm (LLL) for low-complexity lattice reduction aided multiple-input multiple-output (MIMO) detection. The original LLL algorithm performs a swapping with an adjacent column progressively when it doesn't satisfy Lovasz condition. However, this algorithm has a trouble in hardware implementation because its complexity and run-time are variable. This correspondence proposes the modified LLL algorithm which performs a swapping only with the column apart from predefined number of leaping. In the case of the modified column swapping traverse, it clearly decreases the number of iterations and execution time especially for the worst-case situations. Simulation result shows that the proposed LLL algorithm aided MIMO detection achieves more reduced complexity while maintaining similar performance compared to the original algorithm for hardware implementation.