This paper proposes Linear Controller to capture maximum power output in a variable speed wind energy conversion system (WECS). Maximum energy capture from the wind and maintaining constant power supply to the utility grid is necessary. It is obtained by turbine shaft speed control of the system. Matrix converter interfaces doubly fed induction generator (DFIG) with the grid and adjusts generator terminal frequency and thus turbine shaft speed. It also performs power factor control at the grid interface. The design of the controller is to track the desired active and reactive powers delivered to the grid and to adjust the Matrix Converter (MC) control variables. Linear Quadratic (LQ) method is used to design the closed loop state feedback integral controller. Simulation is carried out using MATLAB and the result shows the better performance of the controller to track the reference output and to produce maximum power output.