Metalens are planar lenses composed of the subwavelength arrays, which have unconventional and versatile functionalities to manipulate the light fields compared with the traditional lens. It is noted that the most metalens are designed in a monochromatic mode in the visible or mid-infrared range (mid-IR), however, the broadband range is needed in many practical applications, such as spectroscopy, sensing, and imaging. Here, we design and demonstrate a broadband achromatic dielectric metalens in the mid-IR range of 4 μm - 5 μm for near diffraction-limited (1.0λ) focusing. The broadband achromatic propagation and focusing of the metalens are designed and simulated by constructing and optimizing the phase profile. The Pancharatnam-Berry (P-B) phases of all the elements contribute to the main phase increment of the whole phase profile of the metalens. The additional phase is constructed and optimized by using the random search algorithm to obtain the optimized size of all the elements. The focusing efficiency of the achromatic metalens is also optimized and averaged as the result of phase optimization within a wide band for the building elements, while it is lowered comparing with the regular metalens without broadband achromatic designing. Using this combined designing approach, various flat achromatic devices with the broadband metalens can find a new way for full-color detection and imaging.