A finite element model is created using OpenSees software to perform a time history analysis in order to analyze the seismic response law of a skew bridge and the damage volume of its key components, using a typical 3×20 m skew continuous girder bridge as an example. The seismic response of the skew continuous girder bridge under various factors such as the size of the abutment expansion joint, shear key gap, and shear key strength is studied then the damage rate is assessed for the bearing, shear key, and pier. The research results show that under the action of earthquake ground motion with 0.3 g PGA, the seismic force transmitted to the pier is small, and the pier is elastic owing to the sliding of the bearing, but the damage degree of the shear key is larger than that of the bearing and pier. The impact increases the rotation effect of the main beam in the direction of off acute angle, resulting in a greater damage to the shear key at the acute angle than that at the obtuse angle. The damage of bearing and shear key increases and then decreases with the increasing of expansion joint, and the larger the skew angle is, the smaller the expansion joint will be corresponding to the maximum displacement of bearing and shear key. With the increase of the shear key gap, the deformation limitation effect of the shear key on the main beam decreases significantly, resulting in a linear increase in the bearing slip, which increases the risk of the main beam subsidence. With the increase of the shear key strength, the bearing and shear key damage decreases greatly at first, and then increases slightly. However, the pier damage increases obviously. In an area with a high risk of earthquake, it is recommended that the shear key can be a “fuse element”. For any oblique angle, the shear key gap can be reduced to 2 cm, and the shear key strength can be increased to 125 % or 150 %. When the skew angle is between 30 and 60, the expansion joint size can be increased to 12 cm or 16 cm.