Achromatic metalens have the potential to significantly reduce the size and complexity of broadband imaging systems. A large variety of achromatic metalens has been proposed and most of them have the fixed achromatic band that cannot be actively modified. However, band-tunable is an important function in practical applications such as fluorescence microscopic imaging and optical detection. Here, we propose a bilayer metalens that can switch achromatic bands by taking the advantage of the high refractive index contrast of Sb2S3 between amorphous and crystalline state. By switching the state of Sb2S3, the achromatic band can be reversibly switched between the red region of visible spectrum (650-830 nm) and the near-infrared spectrum (830-1100 nm). This band-tunable design indicates a novel (to our knowledge) method to solve the problem of achromatic focusing in an ultrabroad band. The metalens have an average focusing efficiency of over 35% and 55% in two bands while maintaining diffraction-limited performance. Moreover, through proper design, we can combine different functionalities in two bands such as combining achromatic focusing and diffractive focusing. The proposed metalens have numerous potential applications in tunable displaying, detecting devices and multifunctional devices.