The geometry of a landslide dam is one of the most important factors influencing its breaching process. Understanding how geometric parameters affect breaching is crucial for breach flood assessment and warning strategy development. In this study, numerical simulations were conducted by computational fluid dynamics method to systematically investigate the effect of the landslide dam geometry on the breaching process, with variables including the dam crest length, bottom length, upstream slope angle, downstream slope angle, and channel gradient. The simulation results were calibrated via laboratory tests with a satisfactory agreement. According to the erosion characteristics, the process of landslide dam overtopping failure could be divided into two stages, i.e., headward erosion and overall erosion, and the breach evolution, hydrodynamic characteristics, and erosion processes at the different stages were analyzed. Additionally, the findings indicated that the crest length, downstream slope, and channel gradient all significantly impacted the headward erosion process of landslide dams. At the overall erosion stage, the dam bottom length and maximum lake volume were the key influencing factors. Furthermore, we presented empirical equations to predict the time of headward erosion, time to the peak discharge, and peak discharge at the laboratory scale. Finally, the established empirical peak discharge prediction equations were extended to a dimensionless form, which are applicable to landslide dam failures of various scales. Our study successfully revealed the quantitative relationship between geometric parameters and breaching characteristics, which are beneficial for assessing hazard risk and developing mitigation strategies for landslide dam disasters.