Abstract: Numerical solution of the diffusion equation plays a key role in the study of inertial confinement fusion(ICF). In this paper, based on the global support operator method, a flux-based scheme is proposed. The scheme has local stencil with second-order accuracy both in space and time. For strongly distorted meshes, a procedure of normal direction fix is adopted with proper methods for the computation of corner volume weights, which obtains accurate discretization of the face flux. Numerical experiments show that the scheme can obtain accurate solution for linear problems on non-convex meshes. The method has second-order spatial and temporal accuracy on non-smooth meshes. The method can also preserve the symmetry well and can be extended to the three dimensional unstructured meshes.