The greatest difficulty in deriving the analytical potential energy function of T2O(X1A1) lies in its identity with that of H2O(X1A1) under the Born-Oppenheimer approximation. However, molecular potential energy function is actually a function of internal coordinates， such as bond length and bond angle which correlate with vibration energy, hence with vibration frequency, force constants and isotopic mass. Based on these relations, by using nuclear vibration, rotation, and translation energies to correct electronic energies, the force constants of T2O(X1A1) can be obtained, which represent the difference in masses of isotopes H and T. The calculations are reasonably consistent with reference values. After determining the dissociation limits and dissociation energy and all parameters of two-body terms of T2O(X1A1), the analytical potential energy function has finally been derived by using many-body expansion theory with due consideration of the isotopic effect. The potential energy contours correctly show the equilibrium structure of T2O(X1A1) and the characteristics of the reactions T+OT→T2O and O+T2→T2O. The results lay a sound basis for further researches on reactive collisions.