In this paper, we analyze the transient electromagnetic response from three-dimensional(3-D) dielectric bodies using a time-domain electric field integral equation formulation. The solution method in this paper is based on the Galerkin＇s method that involves separate spatial and temporal testing procedures. Triangular patch basis functions are used for spatial expansion and testing functions for arbitrarily shaped 3-D dielectric structures. The time-domain unknown coefficients of the equivalent electric and magnetic currents are approximated as an orthonormal basis function set that is derived from the Laguerre functions. These basis functions are also used as the temporal testing. Numerical results involving equivalent currents and far fields computed by the proposed method are presented.