Converging slot hole is considered as a high-performance film hole with excellent film cooling effectiveness and relatively low aerodynamic loss. Previous studies on converging slot holes mainly focused on the film cooling effectiveness and heat transfer characteristics, whereas the discharge coefficient has not been fully understood, especially when the compressible effects cannot be ignored. This study numerically evaluated the effects of crossflows and compressibility on the discharge coefficient of the converging slot hole by comparing it with fan-shaped holes, and developed a promising prediction method for the discharge coefficient with both external and internal crossflows. The results show that the crossflow orientations and the compressible external/internal crossflows significantly influenced the discharge coefficients and flow fields of the converging slot hole. The trend of the discharge coefficient of the converging slot hole is obviously different from that of the fan-shaped holes because of the different flow conditions inside the holes. Moreover, the empirical correlations for the discharge coefficient of the converging slot hole based on the no-crossflow data were consistent with the numerical results, validating the numerical methods used in this study.