Based on reaction limited aggregation model, we have investigated the dynamical process of film epitaxial growth in the presence of surfactant. The results ind icate that there are differences between the growth processes of fractal island and compact island. The growth exponents of fractal islands are greater than 1, which that of compact islands are less than 1. On the other hand, “dead" atom d ensity increases linearly with the coverage in the process of the fractal island growth, but the relations between the density and the coverage are nonlinear in the compact island situation.