A multireference coupled cluster (CC) approach formulated in the (2,0) sector of the Fock space (FS) is applied to study electronic states of the Li2 molecule. The CC model including single (S) and double (D) excitations from the reference configuration is considered. The FS-CCSD(2,0) method is applicable to the description of the double electron attached states, which implies that in the neutral molecule studies the doubly ionized reference should be adopted. The results of this study include potential energy curves (PECs) and selected spectroscopic constants for 34 electronic states correlating to five lowest dissociation limits of Li2. Both the PECs and the computed spectroscopic constants agree very well with the experimental data wherever the latter are available. This indicates that the rigorous ab initio method can be successfully applied to study the energetics and molecular properties of the alkali metal diatomics.