Ab initio restricted Hatree-Fock(RHF) calculations, Moller-Plesset correction calculations of the correlation energy, and the density functional theoretical calculations using B3' exchange and Lee-Yang-Parr's correlation functional(B3LYP) with 6-31G^** basic set are compared by optimizing the equilibrium structure of CD₄ and CH₄ and studying their fundamental vibration frequencies. The results are better than HF's, which are obtained by MP2, DFT, MP4 methods. But MP4 method needs too much CPU time. B3LYP is the best choice. The range of relative errors is from 2.0% to 10.4% between the calculated fundamental vibration frequencies and the observed ones.