This Proposed control design Linear Quadratic Gaussian (LQG) for the Grid-Connected and Is-landed mode – Microgrid composed of one network feeding and forming converter with one local load was designed in this paper. The LQG controller is designed for two different Microgrid modes: Grid-connected mode and Islanded mode. A separate LQG controller was designed for each mode and a comparative analysis was made. The LQG controller was designed using the State-Space variables determined by linearizing the model, controller consists of the optimal gain ‘K’, optimal Linear Quadratic Regulator (LQR), and the Kalman Filter. In both Microgrid modes, LQG will eliminate disturbance and noise in the system and makes the system optimal control. The Microgrid system also consists of another control system that comprises the subsequent control subsystem, i.e, Alpha-Beta control, Power and Current loop, and Space Vector Modulation. The steady-state response of the Microgrid system, noise, and disturbance present in the Grid-connected and Islanded mode was rectified by the LQG controller. The design Environment used for developing Microgrid and LQG controller is in the MATLAB / Simulink platform. The effective simulations have permitted and determined results that convey the optimal control and stable performance of the proposed system.