Functional groups on multi-walled carbon nanotubes (MWNTs) were introduced by UV/ozone treatment, reacting with $HNO_3$ alone or with $H_2SO_4/HNO_3$ mixture followed by drying under different conditions. The resulting MWNTs were characterized using a UV-visible spectrometer, SEM, FT-IR, elemental analyzer, and TGA. The amount of oxygen was measured with elemental analyzer and used to check the degree of functionalization on the MWNT surface. Among the various methods tested, the one using $H_2SO_4/HNO_3$ introduced highest amount of carboxyl groups on the carbon nanotubes, while it damaged the MWNTs. Also, even with the similar amount of functional groups, dispersibility of the functionalized MWNTs in water was differed according to the functionalization method. The carbon nanotubes functionalized by reacting with $H_2SO_4/HNO_3$ started to degrade at lower temperature than the ones treated by other methods, which was due to the defects introduced during functionalization.