To address the demand for scroll compressors with enhanced overall performance, this paper introduces a Three-segment Variable-Radius Involute (T-VRI) scroll profile, which combines the advantages of gradually varying and variable cross-sections into a single design. First, a unified mathematical model for the T-VRI is developed using differential geometry, based on the curvature radius function. Following this, detailed formulas for calculating the volumes of the suction and discharge chambers are derived, and key geometric evaluation metrics such as volume ratio, area utilization coefficient, and leakage line length are proposed. Finally, Computational Fluid Dynamics (CFD) simulations of the flow field within the T-VRI scroll compressor are performed using the Pumplinx software. The study's findings indicate that, under identical installation dimensions, the T-VRI profile increases the internal volume ratio by 18.37% and the area utilization coefficient by 9.19% compared to traditional circular involute equal-section profiles, thereby enhancing both volumetric efficiency and material utilization. Additionally, compared to the VariableRadius Involute (VRI) profile with a gradually varying cross-section and the same volume ratio, the T-VRI profile reduces leakage line length by 19.47%. Furthermore, the pressure differentials in adjacent high-pressure chambers and symmetrical working chambers are reduced by 22.16% and 11.55%, respectively, contributing to more stable compressor operation. This research provides valuable theoretical support and methodological guidance for the design of high-performance variable cross-section scroll profiles.