As a prevalent fastening technique in mechanical system assembly, the structural rigidity of screw joints critically governs vibrational response characteristics at both component and full-system levels. In this paper, a new screw equivalent connection stiffness model is established by considering contact stiffness of connector, the meshing stiffness of the thread and the stiffness of the screw and the connected part. Employing fractal-based surface morphology characterization and considering asperity-substrate interaction, an integrated contact load-stiffness formulation for interface morphology is established. Based on the thread stress-strain relationship, the thread axial load distribution law is introduced, the thread meshing stiffness model is derived, and the equivalent model of the screw connection stiffness is established. Finally, the stiffness weakening ratio factor is proposed, and the influence of the combined partial shape parameters on the equivalent connection stiffness is revealed by numerical analysis. The results show that with fractal dimension elevation and roughness amplitude reduction, the equivalent connection stiffness of the screw increases gradually, and the stiffness weakening ratio decreases gradually.