We theoretically deduce the Bragg gap vanishing conditions in one-dimensional photonic crystals and experimentally demonstrate the m=0 band-gap vanishing phenomena at microwave frequencies. In the case of mismatched impedance, the Bragg gap will vanish as long as the discrete modes appear in photonic crystals containing dispersive materials, while for the matched impedance cases, Bragg gaps will always disappear. The experimental results and the simulations agree extremely well with the theoretical expectation.