By using time-domain terahertz (THz) spectroscopy,the THz waveforms emitted from bulk GaAs photoexcited by femtosecond laser pulses under very high electric fields at 10 K have been recorded. It is clearly seen that the THz emission waveforms show a bipolar feature i.e.,an initial positive peak and a subsequent negative dip. Terahertz intervalley transfer gain under step-function-like input electric fields F has been obtained by calculating Fourier spectrum of the measured THz trace under various biased electric fields. We found it can reach 750 GHz for F> 50 kV/cm at 10 K. Furthermore,from the temperature dependence of the cutoff frequency for the gain,it is found that the cutoff frequency is governed by the energy relaxation process of electrons from L to Γ valley via successive longitudinal-optical phonon emission. The estimated cutoff frequencies,at 10 K by considering the time for electrons ballistic acceleration in Γ valley,intervalley transfer,relaxation in Γ valley via longitudinal-optical phonon scattering match the experimental results very well.