The existing connection between the concrete-filled double steel tubular (CFDST) column and the reinforced concrete (RC) beam is difficult to repair and reuse after damage. In this paper, a self-centering joint between the CFDST column and the RC beam is proposed. The self-centering of the joint is realized by prestressed steel strands, and the energy dissipation is realized by friction. The overall purpose of the research is to analyze the influence of steel strand and friction on the mechanical behavior of the joint. By comparing the envelope curve and the restoring force model of a numerical joint model with theoretical values, accuracy of the numerical model was verified. Then, joints with different parameters, including the friction, prestress of steel strands, and ratio of the resisting moment provided by steel strands to the resisting moment provided by friction in the opening moment of joints, were numerically analyzed. The results showed that the joints with greater friction and prestress of steel strands had higher bearing capacity. Increasing the friction could increase the energy dissipation capacity of the joint, but it would increase the residual deformation of the joint. To reduce residual deformation, the prestress of steel strands should be increased. When the resultant force of the pretension of steel strands was greater than friction, the steel head could be kept pressed on the connecting block, making the stress changes of steel strands and the self-centering performance of the joint stable.