Abstract: The density functional theory(DFT)calculations using B3' exchange and LeeYangParr's correlation functional(B3LYP) with 631G** basis set are carried out to study and optimize equilibrium structure and fundamental vibrational frequencies in the equilibrium for CH4, CH3D, CH2D2, CHD3 and CD4. The relative deviation between the calculated and the experimental values is in the range from 1.1％ to 6.3％ for fundamental vibrational frequencies. After scaled, it is in the range of 0.1％and -2.9％. This method is used to predict properties of methane in which some hydrogen atoms are replaced by tritium atoms. Following deuterium or tritium atom number raising in methane the entropy increases, the zeropoint vibrational energy, heat capacity and enthalpy, all reduces.