In this paper, we present an accurate and stable method for the solution of the transient electromagnetic response from the conducting wire structures using the time domain integral equation. By using an implicit scheme with the central finite difference approximation for the time domain electric field integral equation, we obtain the transient response from a wire scatterer illuminated by a plane wave and a conducting wire antenna with an impressed voltage source. Also, we consider a wire above a 3-dimensional conducting object. Numerical results are presented, which show the validity of the presented methodology, and compared with a conventional method using backward finite difference approximation.