Abstract: A simple analysis is made of the superluminal group velocity. The anomalous propagation of an electromagnetic Gaussian pulse through a waveguide with piecewise different dielectric constants is simulated. At the same time, the group velocity and energy velocity of Gaussian wave packet through cutoff region are calculated. And, the "superluminal" problem is analyzed involved in it. From the result of simulating, it is gained that when the length of cutoff region and the work frequency are in one range, group velocity is greater than the light speed in vacuum. But energy velocity is smaller than the light speed in vacuum all long.