Acceleration of a pre-accelerated electron by an ultra-short and ultra-intense laser pulse in vacuum has been explored. The deceleration by the descending part of the laser pulse can be neglected when the pre-accelerated electron is accelerated by the ascending part of the pulse. Because the acceleration dist ance is much longer than for a initially stationary electron, the energy gain is much larger. The net energy gain can be up to 01GeV with a laser intensity of 1019W/cm2 and an initial electron energy of 45Me V. Final energy ga in of the electron as a function of its initial condition and laser parameters h as also been discussed.