The influence of inhomogeneous interaction energy between deposited atoms and substrate atoms on island film growth is investigated by Monte Carlo simulation on a triangular lattice substrate. The Gaussian distribution is employed to describe the inhomogeneity of interaction energy. The results illustrate that the influence of inhomogeneous interaction energy on the growth of thin film is related to the degree of the inhomogeneity and the experimental conditions (such as substrate temperature).At medium temperature the inhomogeneity of interaction energy has notable influence on the island number and the island size. Increasing in temperature could counteract the influence of the inhomogeneity of interaction energy.