By means of transfer matrix method, The complex transmission coefficient through one-dimensional photonic crystal with a dispersive defect which is described by the Lorentz oscillator model is calculated. The equivalent index of refraction defined through the complex transmission coefficient is calculated and the group velocity of an optical pulse with frequency spectrum around the defect mode frequency is investigated. It is found that the equivalent dispersion of the photonic crystals relies strongly on the dispersion of the defect because the transmission spectrum depends sensitively on the optical thickness of the defect which varies with frequency. Since the pulse is composed of a variety of monochromatic field and the transmitted pulse is a re-superposition of all transmitted monochromatic components, the behavior of the pulse propagation is determined by the equivalent dispersion of the medium. Compared with the case that the defect is non-dispersive, the dispersion of the defect layer leads to an ultraslow group velocity. By changing the strength of the oscillator, the group velocity can be changed from subluminal(slower than the vacuum light speed) to superluminal(faster than the vacuum light speed).