We report scanning tunneling microscopy results on the nucleation and growth of Pd nanoclusters on a single layer of graphene on the Cu(111) surface. The shape, organization, and structural evolution of the Pd nanoclusters were investigated using two different growth methods, continuous and stepwise. The size and shape of the formed nanoclusters were found to greatly depend on the growth technique used. The size and density of spherical Pd nanoclusters increased with increasing coverage during stepwise deposition as a result of coarsening of existing clusters and continued nucleation of new clusters. In contrast, continuous deposition gave rise to well-defined triangular Pd clusters as a result of anisotropic growth on the graphene surface. Exposure to ethylene caused a decrease in the size of the Pd clusters. This is attributed to the exothermic formation of ethylidyne on the cluster surfaces and an accompanying weakening of the Pd-Pd bonding.