When the underwater submersible encounters an internal solitary wave (ISW), its loadings and motions are significantly disturbed. To investigate the interaction mechanism between the suspended submersible and the ISW, a three-dimensional ISW–submersible-interaction numerical model was established, based on the computational fluid dynamics (CFD) method. The generation and propagation of the ISW was simulated in a two-layer fluid numerical wave tank, according to the eKdV theory. The standard operation equation of the submersible was introduced to simulate the six degree of freedom (6DoF) motions of the submersible combined with the overset dynamic mesh method. The motion simulation method was effectively validated by comparing it with published experimental results on the motion responses of a slender body under the ISW. Based on the constructed numerical model, the dynamic mechanisms between the suspended submersible and the ISW were studied, and the effects of the initial submerged depths and the ISW amplitudes on the dynamic responses of the submersible were revealed. According to the numerical results, the motions of the submersible have been significantly determined by its initial submerged depths. The submersible located above the ISW interface has a significant motion along the propagation direction of the ISW and its motion trajectory resembles a counterclockwise semi ellipse. The motion of the submersible located below the ISW interface follows the trace of the lower layer of fluid, which presents as an unclosed clockwise ellipse. The corresponding motions of the submersible would be increased with the increase in the ISW amplitudes.