Many frame structures in mechanical equipment are assembled using bolts, and variations in bolt preload can significantly affect the vibration characteristics of these structures, such as the frequency response function (FRF). This paper presents a method for calculating FRF of frame structures considering non-uniform bolt preload, based on the finite element method. A calculation formula suitable for FRF of bolted frame structures is derived based on the definition of FRF and the principle of modal superposition. By using the ANSYS platform, the simulation of bolt non-uniform preload and the extraction method of stiffness and mass matrices for frame structures with non-uniform preload are elaborated, catering to the FRF calculation requirements. The calculation procedure of FRF of bolted frame structure using ANSYS and Matlab is presented. A case study involving a frame structure with four connecting bolts is carried out to validate the proposed FRF calculation method. On this basis, the influence of bolt preload on the FRF of the frame structure is also analyzed through experiments and simulations. Results show that natural frequency and peak values of FRF increase with higher bolt preload.