The creep behaviour of (Ta-Hf-Zr-Nb)C high entropy ceramic (HEC) was investigated at temperatures between 1400 and 1600 °C in vacuum under compressive stresses from 150 to 300 MPa. The measured steady-state creep rates ranged from 2 × 10−9/s to 8 × 10-8/s, which are approximately 10 times lower than the published creep rates of the corresponding monocarbides. The stress exponent n is in the range of 2.34 ∼ 2.89 and the average activation energy is 212 kJ/mol. The creep mechanisms involve dislocation glide/climb and the formation of voids and cracks. The voids formed at the grain boundaries parallel to the loading direction, which often connected to form cracks at the highest load/temperature The active dislocation slip system during creep was <,110>,{111}. The reason why (Ta-Hf-Zr-Nb)C has enhanced creep resistance compared to the monocarbides can be explained by lattice distortion and the higher thermodynamic stability of HEC ceramic at high temperatures.