In recent years, many advances have been made in polarization control and dispersion control of artificial microstructure. However, it is still a challenge to realize achromatic control of arbitrary polarization because the traditional way to calculate the manipulation of metasurface on elliptic polarization have to solve the equation for each piece of data. A direct calculation method based on coordinate transformation is proposed to quickly calculate the manipulation of metasurface elements on arbitrary polarization states. An achromatic focusing metasurface lens based on all-Si elliptic cylinder structure is designed to manipulate elliptical polarization states in the mid-infrared band. The result shows that this method and design can effectively control the elliptic polarization state under the condition of greatly simplifying the calculation process. Compared with the previously reported design based on circular polarization or non-polarization dependence, the application scope of the dispersion control of the metasurface is further expanded.