Abstract: The temporal and spectral properties of Bessel-Gauss pulsed beams with constant diffraction length in a linear dispersive medium are studied. It is shown that by a suitable choice of the spatial parameter β, Bessel-Gauss pulsed beams propagate along the axis without noticeable pulse broadening. If the propagation distance is smaller than the diffraction-free range, temporal pulse forms and normalized power spectra remain unchanged as the diffraction angle increases. However, if the propagation distance is larger than the diffraction-free range, the pulse duration broadens, and the spectra change from blueshifts to redshifts with the increasing diffraction angle.