The bond performance of CFRP to concrete plays a vital role in CFRP strengthening on concrete structures. In this paper, an experimental study was carried out to investigate the bond performance of CFRP to concrete with a convex-circular arc interface. The main factors were the curvature of the concrete surface and the bond length and the layers of the CFRP laminate. Based on the experimental results, the failure mode of the bond specimens, the variation of the bond capacity, the CFRP strain, and the bond–slip constitutive model are analyzed. The results showed that most of the specimens failed to peel off the interface concrete, and the bond capacity tended to increase with the increase in bond length when the bond length was within an effective value. When the interface curvature increased to 1/0.8 m, the bond capacity tended to increase due to the CFRP exerting a certain pressure on the concrete surface. The prediction formula of the bond capacity between the CFRP and concrete is proposed considering the influence of the interface curvature. The bond–slip curves are given out based on the finite differential analysis of the strain distribution of CFRP laminates. The accuracy and applicability of the proposed model are verified with a comparison to the test results and other existing models.