The six-component high-entropy carbide (HEC) (Ti0.2Zr0.2Hf0.2Nb0.2Ta0.2)C has been studied. The electronic structure was calculated using the ab initio VASP package for a 512-atom supercell constructed with the use of special quasi-random structures. The artificial neural network potential (ANN potential) was obtained by deep machine learning. The quality of the ANN potential was estimated by standard deviations of energies, forces, and virials. The generated ANN potential was used in the LAMMPS classical molecular dynamics software to analyze both the defect-free model of the alloy comprising 4096 atoms and, for the first time, the model of the polycrystalline HEC composed of 4603 atoms. Simulation of uniaxial cell tension was carried out, and elastic coefficients, bulk modulus, elastic modulus, and Poisson’s ratio were determined. The obtained values are in good agreement with experimental and calculated data, which indicates a good predictive ability of the generated ANN potential.