In this work, a six-site semiflexible chain model for the polymer reference interaction site model (PRISM) theory was proposed and applied to describe the structure and properties of atactic polystyrene (aPS) melt. In the model, the local monomer structure is composed of six independent sites corresponding to A and B in the backbone and C, D, E, and F in the side phenyl ring group. The intramolecular correlation functions were obtained analytically with the Koyama distribution function and the generator matrix method. To improve the calculation of the intermolecular correlation functions, the potential of mean force was introduced. The calculated X-ray scattering intensity and total radial distribution function were compared with both simulation and experiment data. The results indicate that the model is an effective way to investigate the microscopic structure of styrene polymers.