Based on the theory of atomic and molecular statics, the reasonable dissociation limit for the ground state of TiO is derived.The structural optimization and the frequence analysis for the ground state (X3Δr) of TiO molecule are performed using different density functional theory methods or MP2, MP4 methods with the different basis sets. By comparison with the above calculation results, the conclusion is obtained that the B3LYP method with 6-311+G basis set for O atom and 6-311+ +G** basis set for Ti atom is the most suitable for the geometric structure, vibrational frequence and dissociation energy calculation. The analytical potential energy curve for the ground state (X3Δr) of TiO molecule is scanned using the chosen method, and then fitted to the Murrell-Sortie function using least squares fitting. Finally the spectroscopic constants related to the analytical potential energy function are calculated. All calculation results are in good agreement with the experimental data.