Landslides are a common type of geological hazard. When a landslide collides with a water body, it can generate secondary waves, the destructive potential of which may exceed that of the landslide itself, highlighting the necessity for research on landslide-generated tsunamis. This catastrophic disaster represents a typical fluid-solid coupling process, and the interactions among the two phases significantly complicate the study of this issue. This research proposes an innovative approach to efficiently and effectively simulate this disaster using multi-layer nested grids and a flexible selection of various governing equations. The method couples the progressive landslide model (Ls-Rapid), developed by the International Consortium on Landslides, with the Cornell Multi-grid Coupled Tsunami Model; data conversion between the two models was implemented in Fortran. The effectiveness of this method at different computational scales was validated through case studies of the Gongjiafang landslide in the Three Gorges Reservoir area in 2008 and the 1946 Aleutian tsunami. The simulated results align well with field survey data, demonstrating the promising application prospects of this method in predicting and mitigating landslide-generated tsunamis.