Abstarct: In this thesis, microgrid (MG) frequency control is investigated. Since MGs are composed of various types of distributed generators (DGs) such as wind turbines, photovoltaic systems and energy storage sources which are constantly affected by undesirable disturbances, the frequency stability in the MG is considered to be one of the most important issues and challenges in controlling these systems.Here, in order to control the frequency, model predictive control (MPC) is used. One of the most important chalanges in the implementing of the applied algorithms in MPCs is their computational complexity. Since in MPC control signal is achieved through online solving of an optimization problem, decreasing the required time for solving the problem is of great importance. Active-set algorithm for solving quadratic planning problem is improved by using dual Lagransian theory. According to simulation results, it is observed that these two determinant elements lead to the closed-loop stability and the existence of a solution at all times. Additionally, the projected gradient algorithm is used for decreasing the computational time of solving the problem. Simulation results show that the proposed MPC leads to a faster frequency control scheme in comparison with the classic controllers.