The control of band structures of 2D phononic crystals (PCs) composed of piezoelectric inclusions and elastic isotropic matrix with mechanical/electrical biasing fields is theoretically investigated. The theory for small fields superposed on biasing fields and the plane wave expansion (PWE) method is employed to compute the band structures of the PCs under different biasing fields, including the initial shear/normal stress and the initial electric field. We find that the initial shear stress breaks the symmetry of the material. In consequence, the two bands associated with the level repulsion effect are opened near the apparent crosspoint and form a local band gap. On the other hand, the normal initial stress and the biasing electric field change the effective stiffness and shift the positions of band gaps. The observed phenomena show that the biasing fields can be flexibly used to tune the PC devices.