With the increasing deployment of wind energy technologies, innovative modern control theories, which utilize linear time invariant models, are being developed. The potential for the success of utilizing these theories is better with the availability of concepts such as the variable speed wind trubines. Such control theories are not only capable of increasing the energy capture efficiency of the wind turbines, but also reducing the number of measurements needed which in turn reduces the operation and maintenance costs associated with the system. In this paper, the general formulation of the Linear Quadratic Gaussian Control (LQG) along with the design procedures and the assumptions needed will be stated. Then, a numerical model for the Controls Advacned Research Turbine (CART) that was created and field tested by the National Renewable Energy Laboratory (NREL) will be used to simulate LQG regulator using MATLab script. At the end, the results obtained from the simulation will be presented and the limitations of the LQG controller will be discussed.