For the purpose of investigating the damage mechanism and failure characteristics of tunnel lining under the strike-slip fault movements, a three-dimensional elastoplastic finite element model was established in the present study including a railway tunnel across an active strike-slip fault. With the assistance of this numerical model, the tensile and compressive damage, plastic strain development process, and shear failure of the secondary lining at different fault plane positions were analyzed, and further, the damage laws of the secondary lining at different fault displacement and tunnel-fault intersection angles were summarized. The simulation results showed that when the maximum imposed fault displacement is 30 cm, the most unfavorable fault plane appears at the junction between the moving block and the fracture zone, and serious tensile cracks and shear failures occur on each fault rupture plane. Besides, the maximum plastic strain and compressive damage are distributed in the vault and invert. In addition, with the increase of the fault displacement, the axial strain of the secondary lining increases as well, of which the main part shows the tensile strain. Interestingly, with the decrease of the crossing angle, the axial strain gradually changes from the tensile strain to the compressive strain, which is consistent with the direction of the fault angle. Furthermore, the tensile and compressive damage of the secondary lining increases with the increase of movement distance. At the same time, the tensile damage along the tunnel ring develops, and the compressive damage propagates mainly in tunnel vault and invert. With the decrease of the crossing angle, the degree of the tensile damage in the lining reduces, as well as its range. The compressive damage area of the lining develops from the vault and inverted arch to the tunnel wall on both sides, which has a trend of penetrating the side walls on both sides. The distribution area and maximum value of the overall lining damage indices in tensile (OLDT) and overall lining damage indices in compressive (OLDC) increase with the increase of fault movement distance. With the decrease of the crossing angle, the distribution range and maximum value of OLDT decrease, and the distribution range of OLDC increases, while the maximum value basically remains the same. The research results of the present work can provide reference for the antidislocation design of railway tunnels crossing strike-slip faults.