The density-functional theory (B3LYP, B3P86) and the configuration-interaction method (CCSD(T), QCISD) presented in Gaussian03 program package are employed to calculate the equilibrium internuclear distance Re, the harmonic frequency ωe and the dissociation energy De of 7Li2(X1Σ+g) under a number of basis sets. By comparison with the measurement, the conclusion is that the most accurate Re, De and ωe results (0.2698nm, 1.0487eV and 346.82 cm-1, respectively) can be obtained at the CCSD(T)/cc-PVQZ level of theory. The potential energy curve at this level is calculated over a wide internuclear separation range of 0.15 to 2.7nm at a 0.03nm step size and is fitted to the analytic Murrell-Sorbie function. With the potential obtained at the CCSD(T)/cc-PVQZ level of theory, the rest spectroscopic parameters (ωeχe, αe and Be) are calculated and the values are 2.648cm-1, 0.00702cm-1 and 0.6601cm-1, respectively, which are in excellent agreement with the experimental ones. By solving the radial Schrdinger equation of nuclear motion, the total number of 41 vibrational states has been found when J=0 for this X1Σ+g state. For each vibrational state, the vibrational level, the classical turning point and the inertial rotation constant have been computed, which are in good agreement with the experimental findings. The complete centrifugal distortion constants (Dν, Hν, Lν, Mν, Nν and Oν) are reported for the first time for the first 31 vibrational states when J=0.