We have performed a multicanonical molecular dynamics simulation on a simple model protein. We have studied a model protein composed of charged, hydrophobic, and neutral spherical bead monomers. Since the hydrophobic interaction is considered to significantly affect protein folding, we particularly focus on the competition between effects of the Coulomb interaction and the hydrophobic interaction. We found that the transition which occurs upon decreasing the temperature is markedly affected by the change in both parameters and forms of the hydrophobic potential function, and the transition changes from first order to second order, when the Coulomb interaction becomes weaker.