With the wide applications of three-dimensional (3D) mesh model in digital entertainment, animation, virtual reality and other fields, there are more and more processing techniques for 3D mesh models, including watermarking, compression, and simplification. These processing techniques will inevitably lead to various distortions in 3D mesh. Thus, it is necessary to design effective tools for 3D mesh quality assessment. In this work, considering that the curvature can measure concavity and convexity of surface well, and the human eyes are also very sensitive to the change of curvature, we propose a new objective 3D mesh quality assessment method. Curvature features are used to evaluate the visual difference between the reference and distorted meshes. Firstly, the Gaussian curvature and the mean curvature on the vertices of the reference and distorted meshes are calculated, and then the correlation function is used to measure the correlation coefficient of these meshes. In this case, the degree of degradation of the distorted mesh can be well represented. Finally, the Support Vector Regression model is used to fuse the two features and the objective quality score could be obtained. The proposed method is compared with seven existing 3D mesh quality assessment methods. Experimental results on the LIRIS_EPFL_GenPurpose Database show that the PLCC and SROCC of the proposed method are increased by 13.60% and 6.23%, compared with the best results of the seven representative methods. It implies that the proposed model has stronger consistency with the subjective visual perception of human eyes.