As a combination of the battery-type material and the supercapacitor-type material, lithium-ion hybrid capacitors (LIHCs) can achieve high energy density and high power density. An optimal model is essential to manage the LIHCs effectively for electric vehicle applications. However, modeling of LIHCs has not been systematically investigated. In this paper, the basic dynamic performance of a commercial LIHC is comprehensively analyzed. Two battery-supercapacitor hybrid (BSH) models are proposed on the basis of physical structure and dynamic performance of the LIHC. Meanwhile, nine battery models and two supercapacitor models are systematically compared to determine the optimal model for the LIHC under different temperature conditions. All the model parameters are calibrated with the dynamic response analysis in the time domain. The applicability of the 13 equivalent circuit models (ECMs) under three different temperature conditions are evaluated. According to the evaluation results, the BSH models with highest accuracy and moderate computational complexity are more appropriate for the LIHC behavior description in the electric vehicle operating conditions. This research can well guide the modeling of LIHCs and their state estimator design.