Abstract: Time‑delay has significant influence on the performance of control systems and the stability of controlled structures， which， to a certain degree， limits the application of active control techniques in practical engineering. Although the time-delay classical optimal control method can consider the influence of time‑delay， the time-delay problem needs to be transformed into a delay-free problem through introducing an augmented state vector associated with the control forces within the time-delay interval. Therefore， the augmented Riccati equation needs to be solved， leading to a large amount of computational cost for the design of control law. This paper is devoted to developing a time-delay explicit optimal control method of structures. The explicit time-domain expressions of dynamic responses are first established for the system with time-delay control. On this basis， the time-delay explicit optimal control law can be analytically derived from an unconstrained linear quadratic optimization problem. As the effect of time-delay control force on structural dynamic responses can be readily considered with the aid of the explicit time-domain formulation， the time-delay explicit optimal control law can be derived without augmented treatment of the state vector and solving of the Riccati equation. A numerical example involving a three-storey shear-type structure with an active controller subjected to seismic excitation is presented to investigate the effect of time‑delay and validate the feasibility of the proposed method.