We consider a nonlinear finite volume (FV) method for stationary diffusion equation. We prove that the method is monotone, i.e. it preserves positivity of analytical solutions on arbitrary triangular meshes for strongly anisotropic and heterogeneous full tensor coefficients. The method is extended to regular star-shaped polygonal meshes and isotropic heterogeneous coefficients. The method has been developed in collaboration with K. Lipnikov, M. Shashkov and Y. Vassilevski and is based on ideas proposed by C. Le Potier.