The linings of fault-crossing tunnels in high-seismic-intensity areas are prone to cracking and instability under strong ground motions. Foam concrete damping layers are regarded as effective disaster prevention measures, whereas their anti-dislocation and seismic mitigation performances under strong earthquakes near fault zones remain to be systematically investigated. A subsea fault-crossing tunnel in a bay is taken as the research prototype. A 1:60 scale model test considering fault dislocation is carried out, combined with finite element numerical simulation. Lining stress and deformation are adopted as core evaluation indicators. The influences of elastic modulus, thickness and installation position of foam concrete damping layers on the anti-dislocation and seismic performances of tunnel linings are systematically analyzed, and parametric optimization as well as dual verification are completed. It is shown that the peak dynamic responses of linings are mainly concentrated in fault fracture zones and bimaterial interfaces between the fault and the intact surrounding rock of the hanging wall and footwall. The vault and haunch are identified as the seismic weak positions of linings. Dynamic load transfer paths between surrounding rock and linings can be optimized by foam concrete damping layers, with lining stress and deformation significantly reduced. Elastic modulus and thickness are confirmed as core control parameters for seismic mitigation, while the influence of installation position is limited. Based on the above analyses, the optimal parameter combination of the foam concrete damping layer is determined through multi-case comparative analysis, with an elastic modulus of 75 MPa and a thickness of 20 cm. Compared with the case without damping layers, the peak lining stress is reduced by 39.48% and the peak displacement is reduced by 23.52% under the optimal scheme. Highly consistent results are obtained from model tests and numerical simulations, and the reliability of the optimized parameters is verified. The optimal design parameters of foam concrete damping layers are clarified in this work, and technical references are provided for seismic design and engineering application of fault-crossing tunnels.