Electron acceleration by a chirped Gaussian laser pulse is investigated numerically. A linear and negative chirp is employed in this study. At first, a simple analytical description for the chirp effect on the electron acceleration in vacuum is provided in one-dimensional model. The chirp mechanism is then extended to the interaction of a femtosecond laser pulse and electron. The electron final energy is obtained as a function of laser beam waist, laser intensity, chirp parameter, and initial phase of the laser pulse. It is shown that the electron final energy depends strongly on the chirp parameter and the initial phase of the laser pulse. There is an optimal value for the chirp parameter in which the electron acceleration takes place effectively. The energy gain increases with laser beam waist and intensity. It is also shown that the electron is accelerated within a few degrees to the axial direction. Emphasis is on the important aspect of the chirp effect on the energy gained by an electron from the electromagnetic wave
