Due to the natural dispersion effect of the material itself, chromatic aberration is produced when light is incident, so it is important to eliminate chromatic aberration, especially for metalens. We use the phase change material (PCM) Ge₂Sb₂Te₅ (GST-225) in the wavelength range of 4 to 5 μm and design two-layer vortex metalenses, the first one at a single wavelength of 5 μm, to verify the feasibility of a two-layer metasurface for vortex metalens. The second is a two-layer vortex achromatic metalens, where the two layers are modulated by the propagation phase and geometric phase, respectively, and the design of the vortex achromatic metalens is achieved by a combination of compensation phase and adjustment of the crystallization rate of the PCM. The results show that the designed metasurface achieves achromatic effect in the designed wavelength band, which provides an idea for the design of the achromatic vortex metalens.