The propagation characteristic of ultrashort pulsed Bessel light beam in dispersive medium is studied. The spatially induced group velocity dispersion (SIGVD) can be used to compensate the dispersion of medium. Diffraction-free and quasi-dispersion-free pulsed beams, similar to a spatiotemproal soliton, can be produced in a dispersion medium. The numerical simulation results have confirmed the existence of this soliton-like electromagnetic wave. After considering the finite aperture of Bessel beam and the high-order dispersion, the diffraction-free and dispersion-free propagation can only be achieved in a finite distance. The effect of high-order dispersions would become weaker if the longer light pulses are selected. Within the distance shorter than the diffraction distance, the SIGVD describes accurately the dispersive compensation and evolvement of the pulsed beam.