Two-types of carbon fiber, anisotropic- and isotropic- pitch based, were expose to isothermal oxidation in air and $CO_{2}$ gas and the weight change rates was measured by TGA apparatus. Thc oxidation rate was laster in air than in $CO_{2}$ gas, and the oxidation rare of isotropic T- 101s liher was over 23 9 times faster than that of anisotropic HM-60 filler at $600^{circ}C$ in air. The activation energy was 36-56 Kcal/mole at lower temperature range and 6- 13 Kcal/molc at higher temperature range. It was higher that the transition temperalure 01 reaction zone(zone 1. 2, :i) of 11M-GO fiber than that of T-101s fiber, and it was higher in $CO_{2}$ gas than in air. From SEM observation, it Lvas found that the oxidation of carbon fibers was progressed through the imperfection.