<p>The phenomenon of internal resonance in nonlinear systems is complex and widespread, and it is one of the research hotspots. This paper studies the dynamic response of the three-to-one internal resonance in the supercritical region of the modified axially moving Timoshenko beam. A forced vibration model of the modified axially moving Timoshenko beam considering the shear effect is proposed. The supercritical natural frequencies are solved, and the axial velocity that excites the three-to-one internal resonance is determined. The governing equation is solved by the multi-scale method, and the nonlinear response is obtained. The dynamic solution is solved by the Galerkin method. The results are verified by the Matcont toolbox. By studying the internal resonance responses of the system under harmonic excitation at the first-order and second-order natural frequencies, an interesting phenomenon has been found: under internal resonance conditions, the modal response curve of the first-order resonance exhibits complex multiple jumping phenomena and hysteresis phenomena, while the modal response curve of the second-order exhibits jumping phenomena of two peaks; in the second-order resonance, the coupled two-mode solution is a closed multi-peak curve in both the first-order and second-order modal responses. The dynamic solution of the system exhibits quasi-periodic phenomena, and energy is transferred between the first-order and second-order modes. This study improves the theoretical system of internal resonance of axially moving beams and provides help for its resonance analysis.</p>