The earthquake response of bridge cranes is a very important safety issue for industrial facilities, for example, nuclear plants. During an earthquake, the bridge crane is subjected to multi-impacts and frictional contacts between trolley wheels and girder rails, as well as between crane wheels and runway rails. In this paper, an efficient explicit/implicit transient analysis with Rayleigh damping is proposed in order to take into account frictional contacts with high frequency filtering. For the purpose of reducing computation time, the explicit time integrator, CD-Lagrange scheme, is only applied in the 3D contact areas with a fine time scale satisfying the stability condition, while an implicit time integrator with a large time step and high-frequency Rayleigh damping is adopted in the main part of the crane bridge. High-frequency Rayleigh damping entails a drastic reduction of the critical time step of the CD-Lagrange scheme. As a result, the proposed multi-time step explicit/implicit approach turns out to be accurate and much more efficient in terms of CPU time than the full-explicit approach, in particular when introducing high-frequency Rayleigh damping.