As the span length of bridges and the ratio of component length to thickness increase, the stability issues of large-span steel truss composite bridge structures become more prominent. For this purpose, a large-span steel truss-bridging cable-stayed bridge using both road and rail transport on the Yellow River is taken as a case study. A finite element model is established using the Ansys platform. Whole and local buckling analyses under elastic conditions are conducted, and a stability analysis considering both geometric and material non-linearity is also performed. The research results indicate that the stability of this bridge is primarily controlled by local buckling of the orthotropic integral steel bridge deck, with instability occurring earliest in the partition wall area. In non-linear analysis, geometric non-linearity has a minor impact on the structural stability capacity, while material non-linearity plays a dominant role. The research results presented in this paper can provide references for the stability design and safety assessment of similar large-span steel truss composite bridges.