The paper presents the design and development of a Linear Quadratic Gaussian (LQG) controller for a longitudinal dynamics of a high maneuvering missile. The Linear Quadratic Regulator (LQR) in association with Linear Quadratic Estimator (LQE) is realized through extensive numerical simulations to address theplant dynamics associated with measurement noise and inaccurate plant model. The LQR gives the minimum cost function to the proposed optimal solution for a missile control design application. The LQR and LQE design has been tested for its robustness subjecting it to parametric variation of disturbances and plant uncertainties. The study brings out the efficacy of the LQG controller over traditional methods in missile control system design.