Pulse-type ground motions have special destructive effects on structures, and directivity is one of the fundamental characteristics of velocity pulses. In this paper, the impact of the velocity pulse directivity of seismic motions on both sides of the fault on the seismic response of fault-crossing bridges was quantified using the original records from the Chi-Chi earthquake in Taiwan. First, an automatic baseline correction method was applied to restore the permanent ground displacement, and the direction corresponding to the strongest pulse energy on both sides of the fault was identified based on continuous wavelet transformation. On this basis, the variability of the peak intensity of ground motions on the hanging wall and footwall in different directions, as well as the differences in pulse characteristics between the strongest pulse component and the two initial horizontal components, were analysed. Finally, a typical 5 × 30 m continuous girder bridge was considered as the research object to reveal the influence of the velocity pulse directivity on the seismic response of key parts on both sides of the fault. The results showed that the variability in the peak ground-motion intensity on the hanging wall of the fault was higher than that on the footwall. The displacement variability was up to 863 %, velocity was 262 %, and acceleration was 124 %. The pulse characteristics of the strongest pulse component were stronger than those of the parallel and vertical fault components, and its acceleration, velocity, and displacement response spectra were larger. The amplification effects of the velocity pulse directivity on the transverse bending moment, longitudinal bending moment, and torque of the pier bottom reached 1.3, 1.1, and 1.6, respectively. However, the amplification effect of the velocity pulse directivity on the relative displacement of the pier top, displacement of the main beam, and displacement of the bearing was more than 1.6 times, which was more significant than the internal force of the pier bottom.