This note deals with the problems of fault diagnosis and fault-tolerant control for systems with delayed measurements and states. The main contribution consists in two aspects. First, by solving the Riccati equation and Sylvester equation, an optimal fault-tolerant control law is designed for systems with delayed measurements and states. The existence and uniqueness of the optimal fault-tolerant control law are proved. Second, the physically unrealizable problem of the optimal fault-tolerant control law is solved by proposing a novel fault diagnoser for systems with delayed measurements and states. Finally, a numerical example is given to demonstrate the feasibility and validity of the proposed schemes.