Plasma photonic crystals are composed of plasma and other dielectric materials or vacuum, and have a periodic structure. Their tunable band gap properties enable plasma photonic crystals to be widely used in the manufacture of military medical devices such as filters, plasma cloaks, and plasma lenses. Therefore, it is of great significance to obtain the energy band structure characteristics we need by changing the parameters such as the density and temperature of the plasma. Based on the above considerations, a Petrov-Galerkin finite element method is proposed to solve and analyze the band gap characteristics of plasmonic photonic crystals. The core idea of this method is to construct a basis function space and a test function space whose coefficients are reciprocal of each other on the boundary, and reduce the degree of freedom while eliminating the integral on the boundary. The adopted grid is a semi-Cartesian projected grid, which can adapt to complex plasma column shapes. When the weak form is established, the interface nonlinear continuous condition is linearized, which simplifies the processing of the interface integral term. By drawing the energy band structure diagram of the numerical example, the effects of the plasma electron density, the filling ratio and shape of the plasma photonic crystal column on the band gap width, band gap position, coupling band gap and cut-off frequency are analyzed and verified. Therefore, the controllability of the energy band structure of the plasma photonic crystal can be derived.