The propagation of a Laguerre-Gaussian (LG) beam through a dispersive medium is investigated. The effect of the doughnut-like intensity profile of the probe LG beam on the group velocity is studied. We find an analytical expression for the group velocity out of the optical axis and compare with its projection onto the propagation axis. It is turned out that the group velocity vector is along the optical axis at the waist of the beam and the Rayleigh range. We numerically and analytically investigate the effect of the helical phase front of the coupling LG field on the group velocity of the probe LG field in a four-level double V-type quantum system. Our analysis predicts a strange behavior for the group velocity of the probe LG beam inside a normal dispersive medium in the gain region so that it can exceed the speed of light in free space, leads to the gain-assisted superluminal light propagation in normal dispersion. Such an unusual propagation of the LG beam results from the distortion of its helical phase front via the classical interference of the planar and LG fields. The obtained results may find some potential applications in increasing the velocity of the information transmission in optical communications.