Abstract: The derivation of truncation error on non-uniform grid for cubic spline reconstruction in finite volume framework is analyzed in this paper. The basic rule for the derivation of truncation error on non-uniform grid is proposed which is that all derivations in the truncation error analysis should base on the same stencil. If this rule is not satisfied, the truncation error will not be self-consistent. Furthermore, the third-order discretization of the diffusion terms is obtained based on the correct truncation error analysis which makes both the convection and diffusion terms to achieve consistent third-order accuracy.