As for a two-dimensional function photonic crystal with square structure and point defects, its band gap structure, defect modes and eigenfield distribution of defect modes are studied by using the plane wave expansion method. The refractive index of the dielectric column is chosen as a spatial distribution function, whose coefficients can be adjusted by the altering of the applied electric field and the light field intensities. The research results show that, the adjustability of band gap structure, band gap position, defect modes and eigenfield distribution of defect modes can be realized by adjusting the parameters of the dielectric column, which provides an important theoretical basis and design method for the design of related optical devices.