An analytical model for the tensile stiffness of top-and-seat angle steel connections was proposed based on fundamental mechanical principles aiming at the problem of insufficient prediction accuracy of load-bearing capacity. An explicit functional relationship between the bending stiffness of angle-steel cross-section and the corresponding bending moment was established by utilizing stress integration over the angle steel cross-section and the notion of strain energy equivalence. The force-displacement curves of top-and-seat angle steel connections were obtained based on a realistic "frame model" that better reflected the actual stress state by solving this tensile stiffness model through an incremental-iterative approach. The prediction accuracy and effectiveness of the new model were verified compared with typical published experimental data and the conventional plastic hinge model. The proposed model could reproduce the complete force-displacement skeleton curve of the connection with high fidelity, precisely capturing the smooth nonlinear characteristics of tensile stiffness in elasto-plastic transition zone of angle steel connections. The prediction error of the ultimate bearing capacity was reduced from 23.41% to 6.68% by the new model, and the prediction error of the yield load was improved from 43.16% to 31.60% compared with the traditional plastic hinge model.