The membership relation of intuitionistic fuzzy sets (IFS) does not match interval-valued intuitionistic fuzzy sets (IVIFSs) completely, so it is very difficult for the similarity measure model to match feature conditions perfectly. In this paper, we first utilize the score function and the exact function to describe the characteristic conditions of the interval-valued intuitionistic fuzzy set, and analyse the matching degree of the existing similarity measure models of the interval intuitionistic fuzzy set with the characteristic conditions. Secondly, an interval-valued intuitionistic fuzzy similarity measure model is proposed based on its geometric distance and center of gravity. Finally, its advantage in interval-based intuitionistic fuzzy multi-criteria decision-making is analysed by theoretical proof and empirical research.