This paper proposes a reweighted least squares algorithm for quadrature amplitude modulation (QAM) detector in multiple-input multiple-output (MIMO) channels. Although the QAM detection problem is a non-convex combinatorial optimization problem, it is reformulated into a problem of minimizing the sum of logarithmic functions. In order to find a local optimal solution of the problem, an iterative reweighted least squares (IRLS) based algorithm is proposed. The proposed algorithm is fast real-time applicable due to its low computational complexity. Numerical experiments in a random MIMO system show the effectiveness of the proposed algorithm.