Dispersion characteristics of two-dimensional dispersive and anisotropic-magnetized-plasma photonic crystals are studied using both the plane wave method and finite-difference time-domain method. When the wave vector lies in the periodic plane, due to the external magnetic field, two different regions of flat bands occur in the TE mode. Varying the values of external magnetic field will affect not only the location of flat bands, but also the position and size of band gaps. Increasing the background dielectric constant will make omnidirectional band gaps to be formed, and make the center of gaps reduced while making the width increase. When the wave vector lies in non-periodic plane, dispersion curves of magnetized plasma photonic crystal are no longer divided into TE and TM modes. With the increasing of the non-periodic wave vector, the location of gap shifts upward, and the gap width firstly increases and then varies little.