Abstract: Sub-division method based on support operator is used to solve diffusion equation with three-dimensional non-conformal mesh and non-planar mesh.Numerical experiments show that the method is second-order accurate on general non-conformal mesh.For curved-face mesh and non-planar-face mesh, the method is more accurate than traditional plane-approximation method.For non-conformal orthogonal mesh, the method can obtain accurate solutions of linear problems.