We report in this paper a theoretical study on the quantum thermodynamic properties of a fractional damping system. Through the analysis, few non-trivial characteristics are revealed which include: (i) a fractional power-law decaying entropy function, which provides an evidence for the validity of the third law of thermodynamics in the quantum dissipative region; (ii) the varying of the entropy from a nonlinear divergent function to a semilinear decaying function with a fractional exponent as the temperature approaches to the absolute zero.