One-dimensional nonlinear analysis of wake-field generation and electron bunch acceleration by a chirped laser pulse were investigated numerically. It was found that the optimum linear chirp parameter leads to the wake-field amplitude increase by one order of magnitude and accordingly the acceleration gradient. In our external injection scheme, electrons were accelerated using the initial energy of 100 KeV in=1.2. When the pulse passes through the electron bunch most part of the electrons trapped in the first cycle of the laser wake-field and accelerate to about 1 GeV in 1.8 mm. We concluded that the expensive electron preacceleration mechanism could be omitted in a laser-aided electron acceleration scheme
