As a widely adopted numerical method in recent years, the virtual element method has many advantages. However, when solving some radiation diffusion equations derived from practical problems, the method may not guarantee the non-negativity of the numerical solution or maintain the local conservation property on general polygonal meshes. This paper uses the nonlinear two-point flux approximation as a post-processing procedure, and proposes a positivity-preserving and conservative scheme based on the virtual element method for radiation diffusion equations. The scheme obtains the cell-vertex values of the numerical solution by the lowest-order virtual element method. Then the positive cell-centered values are obtained by the nonlinear two-point flux approximation, where the local conservation property is maintained as well. The numerical results on arbitrary polygonal meshes demonstrate the second-order convergence rate for the solution scheme, and its high adaptability to deal with radiation diffusion problems with strong discontinuous or nonlinear diffusion coefficients.