Ab initio studies of molecular structures and properties of the Li+Ar, complexes were carried out. The investigation of the Li+Ar dimer with the MP2(FULL)/6-311G+(3df) method provides satisfactory agreement with the available experimental data. This conclusion is extrapolated for larger Li+Ar-n (n > 1) clusters which are studied within this level of theory. The reported complexes are stable and deserve the future experimental efforts. The obtained results indicate that the consecutive complexes represent the most symmetrical structures possible with the closing shell for the Li+Ar6 Cation. The dissociation energies as well as interaction energy components follow systematic paths of changes. The reveled clusters are different from their H+Arn predecessors characterized by two solvation shells of 7 ligands total and are also different from Na+Arn clusters for which the single shell may accommodate eight argons. The Ar-Ar interactions do not influence geometries of small complexes but are noticeable in larger structures due to repulsive forces caused by the lack of space around the central cation.