Based on a high level ab initio calculation which is carried out with the multireference configuration interaction method under the aug-cc-pVXZ(AVXZ)basis sets,X=T,Q,5,the accurate potential energy curves(PECs)of the ground state X1∑g+ and the first excited state A1∑u+ of Li2 are constructed.By fitting the ab initio potential energy points with the Murrell-Sorbie potential function,the analytic potential energy functions(APEFs)are obtained.The molecular bond length at the equilibrium(Re),the potential well depth(De),and the spectroscopic constants(Be,ωe,αe,and ωexe)for the X1∑g+ state and the A1∑u+ state are deduced from the APEFs.The vibrational energy levels of the two electronic states are obtained by solving the time-independent Schr?dinger equation with the Fourier grid Hamiltonian method.All the spectroscopic constants and the vibrational levels agree well with the experimental results.The Franck-Condon factors(FCFs)corresponding to the transitions from the vibrational level(v'=0)of the ground state to the vibrational levels(v"=0-74)of the first excited state have been calculated.The FCF for the vibronic transition of A1∑u+(v"=0)←X1∑g+(v'=0)is the strongest.These PECs and corresponing spectroscopic constants provide reliable theoretical references to both the spectroscopic and the molecular dynamic studies of the Li2 dimer.