The effect of methane adsorption on the electronic properties of a lead sulphide (PbS) cluster is investigated using density functional theory (DFT) when an oxygen molecule was previously adsorbed to the cluster. This paper studies how the pre-adsorption of oxygen influences the tendency of PbS cluster to adsorb $\rm{CH}_{4}$ and variations of its electronic properties due to $\rm{CH}_{4}$ adsorption. Further investigation on how these variations occur was carried out by charge transfer calculations. The discussion based on the results of this study succeeded in explaining the previously reported experimental observations.