The electric engine cooling system with the active grille shutter requires intelligent and predictive control to reach its full benefits on fuel economy and thermal management. Conventional control methods regulate the coolant temperature to a fixed value but do not directly minimize the vehicle's fuel/energy consumption. By contrast, we design a fuel minimization controller through solving constraint nonlinear optimization problems, whose cost function is the total fuel consumption and constraints are the vehicle's physical limits. To achieve high computational efficiency and sufficient accuracy, the optimization problem is solved by iterative convex quadratic programming and quasilinearization. The advantages of the proposed control method on both fuel economy and engine thermal management are demonstrated by simulations.