Potential energy curves (PECs) for Li-2 and LiH molecules have been computed by quantum Monte-Carlo (QMC) method in singlet and triplet states. In comparison with CISDTQ, CEPA and CC methods, the most negative total energy values have been obtained by the QMC. The results obtained from this study, include dissociation energy De, vibration-rotation energy levels and spectroscopic constants (omega(e), omega(e)x(e), omega(e)y(e), B-e, alpha(e)) for both electronic states. The obtained D-e values are in good agreement with the experimental values, although the computed D-e for the LiH moiety is one of the most accurate results obtained. (C) 2015 Elsevier B.V. All rights reserved.