A new singularity extraction technique is presented to calculate accurately the singular integrals in Time Domain Electric Field Integral Equation (TDEFIE). In singularity extraction procedure, through the aid of the first order Taylor series of time base function including time-retardation, the singularity of the integrand can be removed. The surface current density and backscattered far-field response of a conducting cube illuminated by a Gaussian plane wave is computed using the presented technique. Comparisons are made with the results obtained by the Inverse Discrete Fourier Transform (IDFT) of the frequency domain and the results obtained by using Vechinskis time averaging technique, which demonstrate that the presented method with this new time domain singularity extraction technique to solve TDEFIE is very accurate and stable.