Toroidal modeling utilizing the non-perturbative magnetohydrodynamic-kinetic hybrid code MARS-K (Liu Y.Q. et al 2008 Phys. Plasmas15 112503), to a DIII-D high-performance discharge with the core thermal ion temperature of Ti ∼ 13 keV, finds multiple branches of unstable internal kink (IK) modes triggered by the bounce resonance of trapped thermal ions. The range of the computed mode frequency aligns well with the bounce frequency of trapped thermal ions, confirming the nature of resonance drive for the instability. The computed mode frequency is close to that observed in experiments. Plasma toroidal flow, in particular the fast flow (10% of Alfvén speed) as in the considered DIII-D discharge, strongly stabilizes the fluid IK branch but not all of the thermal-ion-driven internal kink (TIK) branches, leaving one dominant unstable TIK branch under the experimental conditions. Plasma resistivity also significantly affects stability of the TIKs (but not much on the IK which is ideally strongly unstable) in combination with the drift kinetic drive by thermal ions. High resistivity can drive additional unstable TIK branches. Scanning the on-axis safety factor over a large range confirms robustness of the TIK triggering by thermal ions. The computed TIKs contain both the IK and the tearing components as the dominant contributions to the eigenmode structure. These findings, together with the experimental results reported in reference (Du X.D. et al 2021 Phys. Rev. Lett.127 025001), strongly suggest the possibility of thermal-ion driven instabilities in ITER.