Two-dimensional (2D) monoclinic lattice photonic crystal has potential application for light focusing device and photonic crystal waveguides. In this article, the first Brillouin zone (BZ) and the method of calculating the photonic band gaps of two-dimensional monoclinic lattice photonic crystal are discussed. The photonic band gap (PBG) structure of triangular lattice photonic crystal calculated by the method described in this article agrees well with that from the conventional method. Furthermore, the calculated PBG structure of 2D monoclinic lattice in critical conditions are consistent with either hexagon or rectangle BZ, which shows that the method described here is valid.