As a stable single sheet of carbon atoms with a honeycomb lattice, graphene has become attractive for its potential applications in electrochemical storage devices, such as anodes for rechargeable Li batteries. Since both sides of it can hold adsorbents, a graphene sheet is expected to have extra storage sites and therefore it has a possibly higher capacity than graphite. However, certain shortcomings of Li battery, such as instability lead to battery failure under overcharging or overvoltage conditions. The limit to capacity results in a short time of discharge. Thus, more attention should be paid to the stabilities of electrode materials, such as Li cluster nucleation on graphene leading to dendrite formation and failure of the Li-ion battery. In this work, we build a supercell model of single layer graphene with hexagonal structure, and then change the size of Li cluster which is used to be adsorbed on graphene, with keeping m Li:C ratio at 1:6. Using the first principle based on density functional theory, we calculate the density of states, charge density difference and energy band structure. The interaction between Li and pristine graphene is studied in detail by analyzing the electronic properties and charge distribution of the isolated Li clusters and Li clusters adsorbed on graphene. It is found that the ionic bonding can be formed at the interface between Li clusters and graphene, and the charge transfer controls the interaction of the Li-carbon nanostructure. Combing thermodynamics method with the nucleation mechanism, the relationship between the cluster size and nucleation probability is analyzed, and the nucleation on graphene of Li with a certain concentration is also investigated. We estimate the nucleation barrier for Li on graphene and investigate the stability of Li adsorption on graphene by considering the effects of Li concentration and temperature. The Li concentration of 16.7% is considered for the formation of clusters with different sizes on graphene. With the size of Li cluster increasing, the cluster adsorbed on the graphene begins to be more stable than the single Li atom. The formation energy for the cluster is found to increase with the increase of temperature, and it is negative, meaning that Li cluster can be formed. It is expected that the corresponding calculation results from this atomistic simulation will shed some light on the in-depth understanding of Li-storage on graphene and the cycling stability and dendrite formation in Li-ion batteries with graphene-based materials serving as the anode.