Optimal control problem is typically solved by first finding the value function through Hamilton-Jacobi equation (HJE) and then taking the minimizer of the Hamiltonian to obtain the control. In this work, we propose a new formulation for the gradient of the value function (value-gradient) as a decoupled system of partial differential equations in the context of continuous-time deterministic discounted optimal control problem. We develop an efficient iterative scheme for this system of equations in parallel by utilizing the properties that they share the same characteristic curves as the HJE for the value function. Experimental results demonstrate that this new method not only significantly increases the accuracy but also improves the efficiency and robustness of the numerical estimates. This example will highlight the importance of Eulerian and Lagrangian viewpoints for designing numerical schemes for high dimensional problems in computational math.