In this paper, load frequency control by optimal control algorithm using quasi-Newton method for microgrid introducing diesel generator and battery is discussed. In the proposed method, we consider microgrid model including diesel generator and battery. Also, saturation is taken into account as a constraint on the input to the model of diesel generator and battery. Then, a cost function considering the storage capacity constraint is formulated. Therefore, we propose an algorithm using the quasi-Newton method to determine inputs that minimize the formalized cost function. In addition to the quasi-Newton method, we propose an algorithm using Backward Sweep to match the terminal condition. Finally, we confirm the effectiveness of the proposed method through numerical simulations.