For multiphase (water-liquid, water-vapor, and air) flow in a sharp-edge converging-diverging annulus, when the downstream/upstream pressure ratio is low, the cavitation phenomenon could occur in the contraction area if the liquid pressure drops below its vaporization pressure. The occurrence of the cavitation will contribute to choked flow, affect the local flow velocity field, and limit the flow rate through the annulus, resulting in damages to the annulus surfaces. In this paper, we use the turbulence model (k-ω) and the multiphase models [volume-of-fluid (VOF) and Eulerian] to simulate the liquid-vapor-gas flow with cavitation in the near-closing annulus. The closing percentage of the annulus varies from 50 to 90% in this numerical investigation. This study compares the VOF and the Eulerian models in liquid-vapor-gas multiphase flow computational fluid dynamics (CFD) simulation results. Furthermore, the effect of gas volume fraction (GVF) at the inlet boundary of the computational domain on the cavitation characteristics is analyzed. The analysis of the simulation results suggests that the choked flow rate and the discharge coefficient gradually decrease with the increase in GVF. Conversely, as the GVF grows within the required range (0–20%), the critical pressure ratio for cavitation increases. In this study, we developed data-driven nondimensional models based on such numerical investigations to predict the choked flow rate and the critical pressure ratio in the multiphase (water-liquid, water-vapor, and air) annulus flow. The findings can provide numerical guidance for the experimental design of annulus multiphase cavitation flow and serve as an engineering tool for flow prediction in offshore oil and gas applications.