The dispersion relation of electromagnetic waves in one-dimensional plasma photonic crystals is studied. The plasma photonic crystal is a periodic array composed of alternating thin plasma and dielectric material. The dispersion relation is obtained by solving a Maxwell wave equation using a method analogous to Kronig-Penny’s problem in quantum mechanics, and it is found that the frequency gap and cut-off appear in the dispersion relation. The frequency gap is shown to become larger with the increase of the plasma density as well as plasma width.