A generalized block pulse function (GBPF) is employed to solve a functional differential equation. The operational matrix for integration and the functional operational matrix of the GBPF are introduced to solve the state equation in order to simplify the calculation procedure. The greatest advantage of using a GBPF is that the time interval of calculation can be adjusted arbitrarily. A small time interval is chosen for a steep change of state variable with time and a large time interval is chosen for a flat change of state variable with time. Therefore, the number of expansion coefficients is greatly reduced and the computer time is also minimized when using GBPF compared with the conventional BPF. An illustrative example is given. It is shown that computational results are more accurate for a steep change of state variable using a GBPF rather than a BPF.