In this talk, we will introduce a new kind of high order inverse Lax-Wendroff (ILW) boundary treatment for solving hyperbolic conservation laws with finite difference method on a Cartesian mesh, in which both scalar equations and systems are considered. This new ILW method decomposes the construction of ghost points into two steps: interpolation and extrapolation. At first, we approximate some special points value through interpolation polynomial given the interior points near boundary. Then, we will construct a Hermite extrapolation polynomial based on those special point values and spatial derivatives at boundary obtained through ILW process. This extrapolation polynomial will give us the approximation of the ghost points value. Eigenvalue analysis shows that the new method can improve the computational efficiency on the premise of maintaining accuracy and stability. Numerical tests for one- and two-dimensional problems indicate that our method has high order accuracy for smooth solutions and non-oscillatory property for shock solution near boundary.