In the paper, we consider the ℓ₁-regularized least square problem which has been intensively involved in the fields of signal processing, compressive sensing, linear inverse problems and statistical inference. The considered problem has been proved recently to be equivalent to a nonnegatively constrained quadratic programming (QP). In this paper, we use a recently developed active conjugate gradient method to solve the resulting QP problem. To improve the algorithm’s performance, we design a subspace exact steplength as well as a precondition technique. The performance comparisons illustrate that the proposed algorithm is competitive and even performs little better than several state-of-the-art algorithms.