The behavior of island shape transition and nucleus density evolution in the early stage of epitaxial growth mediated by a monolayer of surfactant is studied by using a kinetic Monte Carlo simulations. The main kinetic processes included in the model are deposition, diffusion of atoms, exchange of adatoms with their underneath surfactant atoms, and reexchange in which an exchanged adatom resurfaces to the top of the surfactant layer. The simulation produces pattern transitions from small compact islands at low temperatures, to fractal-like islands at intermediate temperatures where the deposited adatoms can be easily incorporated into the surfactant layer, and then to regular compact islands at high temperatures where the reexchange becomes active. The island density as a function of temperature exhibits a complex N-shape. These results provide a reasonable explanation for the observed temperature dependence of the growth mode in existing experiments.