Applying the effective-field theory with correlations, we study the phase transition of a periodically diluted Ising system in the presence or absence of a transverse field. We focus on the dependence of the critical temperature of the system on the modulation amplitude and transverse field. The interesting result is: the inhomogeneity of the concentration of magnetic atoms can cause an increase in the critical temperature of the system. However, as the modulation amplitude is increased, the bulk magnetic order of the system may change to a partial magnetic order.