In this paper, new expressions for spot size, radius of curvature, and Rayleigh length of a linearly and negatively chirped Gaussian beam are presented in paraxial approximation self-consistently. It is shown that there is a slight modification in those relations in comparison to that of used in literatures. These modifications change the tailored parameters in some laser beam interactions such as laser electron vacuum acceleration. At propagation distances much grater than the Rayleigh length, the modifications indicate that the temporal shape of the chirped laser beam will be changed. This effect indicates an asymmetric pulse with a slowly increasing front part and a suddenly dropping tail. For propagation distances less than the Rayleigh length, the change in laser pulse shape is not considerable. Finally, the modifications are employed in modeling of a single electron acceleration by the chirped Gaussian laser pulse
