We study heteroepitaxial thin films grown on patterned substrates using a two-dimensional ball and spring model. Island size and its uniformity as a function of patterned substrate parameters and growth conditions are investigated in an early stage of growth using fast kinetic Monte Carlo simulations. In contrast to the flat substrate, patterned substrates provide preferred sites for island formation at the beginning of growth and promote island size uniformity. A patterned substrate parameter enables us to modify island size in a considerable range. Island size uniformity is further enhanced by stress suppression at the island edges when lattice mismatch is increased. Island size, however, decreases as the growth temperature is increased due to the constraint of periodicity of patterned substrates imposed. An upper bound of a patterned substrate parameter before island size becomes less uniform seems to closely connect to island period and island edge spacing of the flat substrate.