Abstract: The evaluation of structural mechanical properties of composite materials is a key problem that needs to be solved urgently in the field of mechanical engineering. In this paper, the material stress and strain data are combined with the cell-vertex Finite Volume Method (CV-FVM) to form a data-driven cell-vertex Finite Volume Method, which is used to solve the complex and costly problem of the composite construction mode. In this method, the stress-strain data of materials are combined with the lattice type finite volume method. By using staggered grid technology, the stress-strain data are defined in the element, and the displacement and Lagrange multipliers are defined in the node, a control body is constructed around the node, and the stress-strain data is allocated to each element. The geometric equations and equilibrium equations of each control body are discrete and solved based on the cell-vertex Finite Volume Method. Finally, the optimal solution of the problem was found by minimizing the extreme distance between the points satisfying the conservation law and the points in the material database. The numerical solution program is developed in C++ language, and the mechanical properties of the square plate with holes of uniform materials and the composite tensile and pressing plate of functionally graded materials are analyzed by the program. The numerical results show that the proposed method is suitable for triangular meshes, bilinear quadrilateral elements and hybrid meshes. The influence of the number of data points, the distance between data points and the value of constant matrix on the calculation results is consistent with the conclusions of finite element method in the existing literature. When the computational cost is similar, the accuracy of the results of the proposed method is close to that of the data-driven algorithm in the finite element scheme, which verifies the effectiveness of the proposed method. Finally, the numerical simulation of functional gradient plate shows that the method has the ability to predict and simulate the mechanical behavior of composite materials.