In this paper the transient electron transport in GaAs bulk is simulated by using ensemble Monte Carlo method. To analyze the transient electron transport the 10000 electrons in the .GAMMA. valley are simulated simultaneously for 10 picoseconds. The electric field-velocity relation is obtained. The high impurity density reduces the negative differential resistance effect. The result of transient average velocity shows the electron velocity in the transient state is faster than that in the steady state. This transient velocity overshoot is caused by the intervalley scattering mechanism. And we confirmed the fact that the energy relaxation time is longer than the momentum relaxation time.