Abstract: Linear quadratic control is one of the basic problems for optimal control, however, its numerical computations still have to be solved. The precise integration of the Riccati matrix differential equations introduced in this paper is very attractive. The analytic characteristics of the Riccati equation is applied to deriving the high precision numerical solution so that the full computer precision is reached. The same method can also be applied to such as Kalman-Bucy filtering, LQG and H∞ control problems. The precise integration method differs from the usual finite difference style method dramatically, and the numerical examples verify the high precision of the solutions. The state vector equation under optimal control is also solved by the precise integration method.