Design method was proposed for self-centering concrete frame joints with energy-dissipation angle steel in this study. Finite element numerical model was established and its validity was verified by experiments. After the joints with different prestressed moment capacity ratios φdes were simulated, the energy dissipation capacity, self-centering performance and material damage under earthquake were studied. Changing the screw gauge distance of angle vertical leg, the measures to improve its energy-consumption capacity were further explored. The results show that the angle energy-consuming joints have perfect self-centering performance, but the energy consuming capacity is slightly insufficient. As the value of φdes decreases, the residual deformation increases and the self-centering ability decreases, but the energy dissipation capacity increases. Therefore, compared with the hybrid connection joint, the minimum φdes value of joint should be appropriately reduced to make up for its insufficient energy dissipation. The plastic deformation of the angle vertical leg is the main energy dissipation mode of the joint, concentrating on the height of the bolt hole and the turning of the vertical leg. If the distance between the vertical screws is reduced and the other material parameters keeps constant, it will lead to decrease in φdes values, increase of the bending capacity of the section and growth of the energy dissipation capacity of the joint.