We present an electron-identification method using the time-projection chamber and the lead-glass calorimeter in the TOPAZ detector system. Using this method we have achieved good electron identification against hadron backgrounds over a wide momentum range in the hadronic events produced by both single-photon exchange and two-photon processes. Pion-rejection factors and electron efficiencies were 163 and 68.4\% for high-\(P_T\) electrons and 137 and 42.7\% for low-\(P_T\) electrons in the single-photon-exchange process, and 8600 and 36.0\% for the two-photon process, respectively.