Because of the existence of velocity pulse, the dynamic response of structure under near-fault and far-field earthquake may be different. Taking the equivalent pier of a typical railway bridge built in deep-water as an example, the vibration characteristic and dynamic response under the two kinds of earthquake were contrasted based on the potential-based fluid method from fluid-structure interaction theory. The research results show that, the vibration characteristic of pier is changed because of the water around it. With the increase of the depth of water, the natural vibration period of pier becomes larger and the first period increases by 10.4% when the water depth is 30m. The distribution of hydrodynamic pressure along the pier is parabolic, which is larger by near-fault earthquake, and the difference becomes more obvious with the addition of water depth. There is also significant difference between the dynamic response under near-fault and far-field earthquake, in addition, the dynamic response under near-fault ground motions is greater than that of far-field earthquake.The diplacement at the top of pier, the moment and shear force at the bottom of pier increase by 34.5%, 37.8% and 51.3% respectively under near-fault earthquake; while these three indicators are 17.0%, 21.8% and 40.0% for far-field earthquake. In summary, the destructive capacity of near-fault ground motions with obvious velocity pulse is far greater than far-field earthquake, so special attention should be paid to those bridges surrounded by deep-water in near-fault zone.