To improve the material utilisation efficiency, a new type of arch-cable composite bridge was proposed based on the tied-arch bridge and beam string structure. Then, the stress mechanism of this system, as well as its deformation and stress under vertical loading, were analysed. Arch-cable composite bridges use arch ribs and main cables as their main load-bearing components. The main cable anchors are fixed to the arch springing in place of the tie rods employed in tied-arch bridges. The main cable is not only used to balance the thrust of arch springing but also directly bears dead and live loads. Theoretical analyses show that, in arch-cable composite systems, when the bending moment of the vault is zero, the ratio of dead load carried by the arch and the cable equals the ratio of the rise of the arch to the cable sag. In light of this situation, a simplified mechanical model of the arch-cable composite bridge was established to derive the analytical equations for the vertical deformation of the structure, as well as the bending moment of the arch rib and the horizontal force of the main cable under the impact of concentrated load and full-span uniform load. Subsequently, a finite element model (FEM) of the arch-cable composite bridge was established to verify the theoretical equations. The finite element simulation results are consistent with the theoretical values. Furthermore, a tied-arch model with the same span was established to compare and analyse the stress differences between its main members and those of the arch-cable composite bridge model. Results show that, compared with the tied-arch bridge, the arch-cable composite bridge bears fewer stresses on the arch rib, main cable and hangers, showing greater structural stiffness and excellent structural performance.