To rationally evaluate the seismic damage of RC structures comprehensively and multi-dimensionally, a damage index calculation method is proposed. This is a macroscopic global seismic damage model that considers torsional damage, damage in two perpendicular horizontal directions, as well as the overall damage, based on the modal characteristics of the three-dimensional structure and the multi-mode damage model. Formulas are derived, and the steps for damage evaluation are summarized. To better illustrate the results of the proposed method, an example of an asymmetric 6-story frame-shear wall structure is built using the OpenSees program. Thirteen ground motions are selected for incremental dynamic analysis. The structure’s damage indexes are evaluated according to the proposed method and compared with the corresponding structural responses, He et al.’s index, and the Final Softening index. The results demonstrate that the proposed method can fully reflect the macroscopic damage state of the structure from different perspectives. Additionally, the results show that, despite the ground motion only acting in the y-direction, the structure exhibits responses and damage in both the x-direction and the torsional direction. The overall damage to the structure is primarily controlled by the torsional damage, attributed to the asymmetric arrangement of shear walls. The torsional effect is the key factor leading to the failure of asymmetric structures during earthquakes. Therefore, ensuring the torsional strength of the structure is crucial during the structural design process.