In this paper, the dynamic characteristics of electron acceleration by a chirped Gaussian laser pulse are studied regarding the synchronization between the axial force phase and electron. Linear, circular, and elliptical polarizations are employed in this investigation. It is found that the chirp parameter plays an important role in the phase synchronization procedure. In this numerical study, the accelerated electron could acquire several tens of GeV energies from a very intense chirped laser pulse. It is also found that the electron final energy is very sensitive to the state of the wave polarization
