Mercaptoundecanoic acid (MUA) has been used to enhance the dispersity of Au nanoparticles in organic solvent and the affinity between the Au nanoparticles surface and titanium dioxide shell in the synthesis of $Au/TiO_2$ core-shell composite nanoparticles. The dispersity of the MUA-coated Au nanoparticles in ethanol aqueous solution with different concentration of $H_2O$ was investigated by UV-Vis. absorption spectrum and the coating amount of MUA was varied from 0.02 mM to 1.0 mM. The MUA-coated Au nanoparticles were highly dispersed in pure $H_2O$ in the wide range of the coating amount of MUA. On the contrary, the MUAcoated Au nanoparticles showed an enhanced stability in the ethanol/$H_2O$=8/2 mixed solution only when the coating amount of MUA was 0.05 mM, and in the ethanol/$H_2O$=7/3 mixed solution when the coating amount of MUA was in the range from 0.02 mM to 0.17 mM. From this systematic study, it can be inferred that the stability and the dispersibility of Au nanoparticles in organic solvents are highly sensitive towards the amount of MUA coating.