Based on analyzing the dispersion characteristics and global band gaps for general two-dimensional Photonic Band Gap (PBG) structures formed by triangular arrays of metal posts for TE modes, two methods are proposed to solve the problem of the high Q value in PBG cavity. The result shows that the Q value can be effectively controlled by loading media structures or inserting dielectric perturbation in PBG cavity. In consideration of mode competition in PBG cavity, the mode selection is calculated respectively for the two methods. It is shown that the two methods both can control the Q value without reducing the mode selection or changing the electric field distribution of TE04 mode. In addition, two competing modes are cleared in the method of dielectric perturbation, which improves the mode selection at the operation frequency of TE04 mode.