We present a method for computing the solution to the infinite horizon continuous-time constrained linear quadratic regulator (CLQR). The method relies on two main features: a multi-grid 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 grid 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. We present two examples, a single-input single-output unstable system and a three-input three-output stable system, to show the main characteristics of the proposed computation method.