  We study the propagation of a Laguerre-Gaussian (LG) beam through a
dispersive atomic medium. We restrict ourselves to applying a weak probe field
and three strong coupling fields to the medium, which leads to developing a
four-level double $V$-type atomic system. We first regard all the three strong
coupling fields as the plane-waves and calculate an analytical expression for
the group velocity of the probe LG field on the optical axis at the waist of
the field. It appears that the resulting formula in a dispersive medium is in
good agreement with that of the free space. We also find a more general
analytical expression for the group velocity of the probe LG field out of the
optical axis and compare with its projection onto the propagation axis. It is
turned out that these two quantities are equal on the optical axis, at the
waist of the beam and the Rayleigh range. Finally, we assume one of the strong
coupling fields to be an LG field and explore how its orbital angular momentum
(OAM) affects the group velocity of the probe LG field. Our analysis predicts a
strange behavior for the group velocity of the probe LG field inside a normal
dispersive medium so that it can exceed the speed of light in free space. Such
an unusual propagation of the LG light beam results from the distortion of its
helical phase front via the classical interference of the planar and LG fields.
