This talk concerns the classical total variation (TV) image deblurring problems, which involves an unconstrained minimization problem consisting of a least-squares term and a total variation regularization term. We transform the original unconstrained problem into an equivalent constrained problem, and use an augmented Lagrangian method to handle the constraints. The transformation allows the differentiable and non-differentiable parts of the objective function to be treated using separate subproblems. Each subproblem may be solved efficiently and an alternating strategy is used to combine the solutions. The new algorithm is faster than several state-of-the-art TV algorithms.