Concrete is widely used in various large construction projects owing to its high durability, compressive strength, and plasticity. However, the tensile strength of concrete is low, and concrete cracks easily. Changes in the concrete structure will result in changes in parameters such as the frequency mode and curvature mode, which allows one to effectively locate and evaluate structural damages. In this study, the characteristics of the curvature modes in concrete structures are analyzed and a method to obtain the curvature modes based on the strain and displacement modes is proposed. Subsequently, various indices for the damage diagnosis of concrete structures based on the curvature mode are introduced. A damage assessment method for concrete structures is established using an artificial bee colony backpropagation neural network algorithm. The proposed damage assessment method for dam concrete structures comprises various modal parameters, such as curvature and frequency. The feasibility and accuracy of the model are evaluated based on a case study of a concrete gravity dam. The results show that the damage assessment model can accurately evaluate the damage degree of concrete structures with a maximum error of less than 2%, which is within the required accuracy range of damage identification and assessment for most concrete structures.