Band gaps of both TE-polarized and TM-polarized modes photonic of two-dimensional triangular-lattice ellipse-lattice-points air-hole photonic crystal are caculated by finite element method. By changing the size and direction of ellipse lattice point air holes, the effects of air hole filling ratio and lattice points direction to the photonic band gaps are studied. The results show that TE-polarized mode band gaps are easier to be formed in air-hole photonic crystal. With different filling ratio, lattice point direction has different effect on both TE-polarized and TM-polarized modes band gaps. There is no complete photonic band gap no matter where lattice points orient.