A linear time-delay state equation is solved by the proposed generalized orthogonal polynomial (GOP) method. The parameter identification of such a system with time delay is also studied. The system is partitioned into several time intervals. Within a certain time interval, the state and control functions are assumed to be expressed by the GOP series. Time-delay differential equations are transformed into a series of algebraic equations of expansion coefficients. An effective algorithm is proposed to solve the time-delay system problem and to estimate the system parameters. By using such an effective computational algorithm, the calculation procedures are greatly simplified. Two illustrative examples are given to demonstrate the validity of the method. Very accurate results are obtained.