Gaussian pulse has no beginning point, so has no Laplace transform and is non-physical. We propose sinnt pulse (referred to as pseudo-Gaussian pulse or PGP) as an approximation of the Gaussian pulse. PGP has the Laplace transform and approaches the Gaussian pulse as n→∞. The propagation of PGP-modulated wave packet in the highly anomalous dispersion band of a Lorentz medium is investigated by numerical inversion of Laplace transform. Our results are greatly different from the conventional results obtained by the saddle point method. Our results show that the velocity of a Gaussian wave packet cannot be explained only by the concept of the group velocity as has been done so far.