In order to study the frequency range of the negative refractive index of the photonic crystal, the band gap structure of the two-dimensional photonic crystal is solved by analyzing the numerical value based on the finite element algorithm. This process involves how to design the mathematical and physical models, design the solving equation of the finite element algorithm, and the numerical results were physically analyzed. First, the finite element algorithm is used to calculate the points in the wave vector space of all relevant frequencies in the Brillouin region to plot the isofrequency surface. Then, the isofrequency surface under different air hole radii is drawn. Finally, the frequency interval between the negative refractive index can be obtained by finding the direction with negative group velocity on the structure of the isofrequency surface. At the same time, comparing the influence of different air hole radii on the frequency range of the negative refraction of photonic crystals can provide support for the preparation of photonic crystal devices.