In a coherent optical communication system, a polarization fluctuation of an optical fiber is one of the most important problem. On the other hand, for a realization of optical devices, dielectric waveguides with sinusoidally varying width are investigated. Knowledge of the electromagnetic field distribution in a dielectric waveguide with boundary perturbed time by time becomes a very interesting problem. This paper shows a numerical method to simulate the effect of the external disturbance against the dielectric waveguide from time to time. The author has discussed body fitted grid generation with moving boundary for the Poisson's equation and the Laplace's equation. Here we apply this theory for the dielectric waveguide. The technique employs a kind of an expanded numerical grid generation. As the author added time component to grid generation, the time dependent coordinate system which coincides with a contour of moving boundary could be transformed into fixed rectangular coordinate system. Two cases of the perturbations against the dielectric waveguide are treated. In the first case, we present the electric distribution in the dielectric waveguide perturbed along a propagation path. While in the second case, the electric field in the waveguide perturbed perpendicular to the propagation path. Such phenomena that the phase of the electric field modulated by the external perturbation are clarified by numerical results. This technique makes it possible not only to analyze the effect of the external disturbance in a coherent optical communication system but also to fabricate optical modulators or couplers.