The self-anchored arch-suspension bridge is characterized by innovative structure and beautiful shape. In order to research the mechanical characteristics and stability of this structure that has never been built, the proposed preliminary design of the combined system bridge with a main span of 406m is studied. On the basis of the transfer mechanism of live load based on the deflection theories of suspension bridges and arch bridges, the stability of the combined system bridge is analyzed in this paper. The universal finite element software ANSYS is applied to study the linear elastic stability and the geometrically non-linearity stability under six load cases. The study indicates that the transfer mechanism of live load is determined by the distribution of the stiffness. There is no possibility of in-plane instability under live load. The first-order linear elastic instability mode shows the shape of lateral flexure of the junction at mid-span, and the geometrically nonlinear stability is controlled by the lateral flexure. These conclusions can be of some value for the design, calculation and operation management of this structure.