In the construction of large-span concrete-filled steel tube (CFST) arch bridges in complex terrain and harsh conditions, the construction of traditional welded joint connection of arch ribs is of high difficulty and unstable quality assurance. To address this, a new bolt-welded joint connection was proposed, which effectively reduced the difficulty of joint construction and ensured the quality of the joint. Furthermore, by using the rigid-frame (composite member) composed of CFST with the new bolt-welded joint and the outer reinforced concrete as the ribs of the arch bridge, the bearing capacity of the entire structure was improved, along with the adhesive property between the steel tube joint and the outer concrete, offering broad application prospect. Given the characteristic of small eccentric compression in arch ribs, this study investigates the mechanical performance of composite members with the new bolt-welded joint through eccentric compression tests. The mechanical differences between the composite members with different connection forms (welded joint and bolt-welded joint) were compared, and the finite element analysis was performed to further discuss the mechanical behaviour of composite members and effects of the design of the bolt-welded joint. The results indicate that the inner CFST of composite members primarily contributes to the bearing capacity under small eccentric compression. Increasing the amount of the reinforcements in the outer concrete can effectively improve the bearing capacity of composite members. New bolt-welded joint can provide superior joint performance for composite members while ensuring the safety of joint construction, which enhances the stability of the joint and improves the interaction with the outer concrete, further ensuring bearing capacity and improving ductility of composite members. When adopting the bolt-welded joint for CFST connections, the bolt-welded arc length ratio should be within 2.00.