The optimal control problem for linear time-varying systems affected by external persistent disturbances with known dynamic characteristics but unknown initial conditions is consider and a design procedure of a feedforward and feedback optimal controller is presented. The condition of existence and uniqueness of the control law is given. The disturbance observer is proposed to make the feedforward control law realizable physically. Simulation results demonstrate that the feedforward and feedback optimal control law is more effective and robust than the classical state feedback control law with respect to external disturbances. The optimal control problem for linear time-varying systems affected by external persistent disturbances with known dynamic characteristics but unknown initial conditions is considered and a design procedure of a feedforward and feedback optimal controller is presented. Simulation results demonstrate that the feedforward and feedback optimal control law is more effective and robust than the classical state feedback control law with respect to external disturbances.