A new source which has a bandpass spectrum has been proposed for the FDTD analysis of waveguide discontinuity. Compared with the Gaussian pulse source, a significant computational time saving is achieved by using the new source. The new source can filter out all undesired frequency components. With this excitation scheme, the whole system of investigation can operate under the predesigned frequency band, and stability can be quickly reached in the FDTD calculation. In addition, by using the new source, the FDTD calculation can prevent the effect of unabsorbed frequency components which often requires a sufficiently large computation region. To demonstrate the validity and efficiency of this source scheme, numerical results for a rectangular waveguide containing a dielectric layer are given, compared with the data of Gaussian pulse excitation that have been published.