Steel structures strengthened with CFRP (carbon fiber-reinforced polymer) composite may encounter extreme load such as earthquake or impact which may cause steel yielding and plasticity. But very limited investigations exist on the effect of steel yielding on the bond behaviour between CFRP and steel. This paper presents a comprehensive study on the effect of steel yielding on the bond behaviour of CFRP-steel double strap joints. Firstly, a stress-based analytical model is established for the analysis of the ultimate load and failure initiation position of the double strap joints. This is a universal model which is able to analyse elastic joint as well as plastic joint with steel yielding. Then a series of tensile tests with double strap joints is carried out and the experimental results are used to validate the proposed analytical model. Finally, a parametric analysis is performed using the analytical model and an additional numerical method in which the debonding between steel and CFRP strips is simulated by a cohesive approach. The parametric analysis considers both geometrical and material variables. It can be concluded that the steel yielding has a significant effect on the bond behaviour of CFRP-steel double strap joints, including ultimate load, stress and strain distributions of CFRP, steel and adhesive, and debonding initiation position of the joint. Based on the experimental and analytical results, criteria are proposed for the determination of effective bond length and yielding bond length, debonding initiation position and ultimate load of CFRP-steel joints.