The dispersion relations of the triangular plasma photonic crystals in TE mode and TM mode were calculated by finite element method. The influences of plasma filling fraction on the band positions and band gap widths were analyzed. The results show that the plasma photonic crystal has two unidirectional band gaps in M-Γ and X-M directions, respectively in TM mode. With increasing of the filling fraction, the bands shift to higher frequencies, and the band gap widths increase and finally reach a stable value. In the TE mode, the plasma photonic crystal not only has a unidirectional band, but also has the flat bands with low frequencies, which are the surface plasma waves. A complete band gap forms at the large filling fraction, and the band gap widths increase with increasing of the filling fraction. An effective way for fabrication of tunable plasma photonic crystals is provided, which may find wide applications in the manipulation of microwaves or Terahertz waves.