To determine the guide operating band, we derived the eigenvalue equations for a two dimensional photonic crystal rectangular waveguide, and found that the E(y), TEy, H(y) and TMy modes can exist in the photonic crystal rectangular waveguide. The calculation explains that this kind of waveguide can operate in single mode, if the height of the waveguide is low enough. And the bandwidth when the waveguide operates in single mode is determined by the cutoff frequency of the E(y)1 mode and that of the E(y)2 mode.