We propose in this note a method for computing the solution to the infinite horizon continuous-time constrained linear quadratic regulator. The method is based on two main ingredients: a multigrid method for placing a finite number of time intervals, and a piece-wise linear parameterization of the input within the intervals. The input values at the decision-time points and slopes within the time intervals are computed via quadratic programs (QPs). The grids are gradually refined to efficiently improve the accuracy of the solution, and the required matrices and vectors for all QPs are computed offline and stored to improve the online efficiency. Two examples are presented to show the main characteristics of the proposed method.