In the case of unreinforced concrete structures that utilise H-shaped steel as a skeletal framework, concrete specimens integrated with H-shaped steel were prepared to represent varying degrees of corrosion, specifically rates of 0%, 5%, 10%, 15%, and 20%. Push-out tests were conducted to analyze the bond stress-slip relationship between H-shaped steel and concrete under different corrosion levels at the interface. This paper sets out an experimental method to derive the distribution of bond stress across the steel-concrete interface. The method involves measuring the compressive displacement on the surface of the concrete. It is evident from the observations derived from the experimental tests that four microscopic mechanisms are postulated to elucidate the impact of corrosion on the bond performance of H-shaped steel in concrete. A constitutive relationship was constructed, incorporating the effect of the corrosion rate on bond stress-slip, and an interface damage parameter was introduced to analyze the evolution of interface damage under varying corrosion rates. The research results indicate that the initial bond stiffness at the H-shaped steel-concrete interface increases with the corrosion rate. Nonetheless, upon attaining peak stress levels, the rate of decline in interface stiffness is observed to accelerate concomitantly with an increase in corrosion rate. It is noteworthy that at elevated corrosion rates (≥15%), the bond-slip curve manifests a dual-peak feature, initially ascending, then descending, followed by an additional rise, and ultimately a decline. As the corrosion rate increases, the roles of chemical bonding and microscopic mechanical bonding become more dominant, while the contributions of macroscopic mechanical bonding and rust interface bonding diminish. The developed constitutive relationship, validated through comparative analysis with existing models, accurately describes the bond characteristics at the corroded H-shaped steel-concrete interface. Although an increase in corrosion rate hastens the reduction of interface stiffness, its influence on the extent of damage observed upon specimen failure is relatively limited.