The occurred damages during the past significant earthquakes have proved that vertical seismic excitation has tremendous effect on bridges. Three-component earthquake excitations are preferred to resemble the earthquakes. In this article, a cable-stayed arch bridge, a new type of bridge with the hybrid system of half-through arch and stay-cables, was analyzed under a set of different earthquake excitations (more than 21 ground motion records). Both vertical and horizontal components of the ground motions were considered to act simultaneously at the bridge supports. By using different three-component earthquake excitations, the dynamic responses of the bridge, including the displacements and accelerations of the main parts of the bridge, were obtained. The effects of various parameters such as soil type, epicentral distance, spatial variation of the ground motions, and dimensional variation of the structure were investigated. The results of the numerical study indicate that the cable-stayed arch bridge subjected to both horizontal and vertical components of earthquakes are more vulnerable than those subjected to horizontal ground motion only.