It is a common situation that seismic excitations may lead to collisions between adjacent civil engineering structures. This phenomenon, called earthquake-induced structural pounding, may result in serious damage or even the total collapse of the colliding structures. Filling the gap between two buildings erected close to one another by using visco-elastic materials can be considered to be one of the most effective methods to avoid seismic pounding. In this paper, a new polymer–metal composite material made of polyurethane and closed-cell aluminum foam is proposed as a pounding energy absorber for protection against earthquake hazards. The composite was created in two versions, with and without an adhesive interface. A series of experiments which reflect the conditions of seismic collision were performed: quasi-static compression, dynamic uniaxial compression and low-cycle dynamic compression with 10 loops of unloading at 10% strain. The composite material’s behavior was observed and compared with respect to uniform material specimens: polymer and metal foam. The experimental results showed that the maximum energy absorption efficiency in the case of the new material with the bonding layer was improved by 34% and 49% in quasi-static and dynamic conditions, respectively, in comparison to a sole polymer bumper. Furthermore, the newly proposed composites dissipated from 35% to 44% of the energy absorbed in the cyclic procedure, whereas the polymer specimen dissipated 25%. The capacity of the maintenance of the dissipative properties throughout the complete low-cycle loading was also satisfactory: it achieved an additional 100% to 300% of the energy dissipated in the first loading–unloading loop.