Abstract: Prony's method has been combined with time domain integral equation (TDIE) to solve transient response from arbitrary thin wire structure. Early-time response is calculated by TDIE. Prony's method is used to extract the pole from early-time response, the late-time response can be calculated efficiently. The present method avoids tedious computations in conventional TDIE, the efficiency of solving the transient response is speed up greatly. The current distributions on conducting straight wire and a circular loop excited by a Gaussian pulse are computed.