The influence of the beam size of pulsed laser on damage morphology of absorbing glass, as well as the mechanism of the damage produced by high-repetition-pulsed laser (kHz magnitude), is investigated. We show that the damage morphology changes greatly with the decrease of the beam size under the condition that the energy of each individual pulse,the number of the pulses incident on the glass and the repetition frequency are kept invariant. The damage is induced by melting of the glass material due to dispersed energy of the incident laser with large beam size. With decreased beam size of laser, the material will break resulting from the melting and evaporating of glass induced by the densing and increasingly deposited laser energy in glass material. When the beam size is further reduced, too intensive laser will penetrate the dielectric material on the surface of glass. As a result, the laser induced plasma shock wave occurs. In addition, the super-heated liquid at the center where the laser beam interacts with glass will be produced as a consequence of the tremendous deposited laser energy. When the threshold of phase explosion is reached, the mixture of the evaporated, melted and original solid materials will blast outwards. Consequently, characteristic morphology made up of three regions covered with solid granules of original glass material and the re-crystallized material of the evaporated and melted glass will form around the damage crater.