Based on the group theory and the theory of atomic-molecular reaction statics, the reasonable dissociation limit for the ground state (X2) of TiN molecule is derived. Optimization calculation is performed using different groups of density functional method including BP86, B3P86, B3LYP, B3PW91 with different basis sets. The results show that the BP86 method with D95V++ (d, P) basis set for nitrogen atom and 6-311++G** basis set for titanium atom is the best group for calculating the geometric structure, the vibration frequency and the dissociation energy. The potential energy curves and the relevant spectroscopic constants for the ground state of TiN are obtained by least square fitting to the Murrell-Sorbie analytical potential function. All calculation results are in good agreement with the experimental data.