The photonic bands of a one-dimensional photonic crystal containing epsilon-near-zero metamaterials are investigated both theoretically and numerically. A theoretical expression of the edge frequencies of the photonic bands derived from the dispersion relation of the photonic crystal is in excellent agreement with the edge frequencies of the photonic bands calculated using the plane wave expansion method. These results are also confirmed using the transmittance obtained from the transfer matrix method. The theoretical expression of the band edge frequencies indicates that the magnitude of the bandgap increases as the frequency increases in the lower bands and becomes saturated in the higher bands. This is because the bands become flat in the higher frequency range.