This paper studies the l(q)(0 < q < 1) regularized least squares regression (l(q)LS) problem, which arises in many applications of signal processing and machine learning. The iterative thresholding algorithm is an important algorithm for solving the l(q)LS problem, and can be viewed as a Jacobi-type iterative method. This paper proposes a Gauss-Seidel version of iterative thresholding algorithm called GAITA for solving the l(q)LS problem. Under certain conditions, we establish its global convergence(1), eventual linear rate, and the convergence to a local minimizer. Compared to the Jacobi counterpart, the proposed algorithm can allow larger step sizes and converge much faster. The effectiveness of the proposed algorithm is justified with numerical experiments on both synthetic data and real data. (C) 2017 Elsevier B.V. All rights reserved.