A new plasmonic nanofocusing metalens based on aperiodic silica grating arrays was designed and investigated. Assisted by the graphene surface plasmon, the infrared polarized light can be focused in a nanospot with a dynamically controlled focal length by varying the dielectric strip width or the graphene Fermi level Ef. For instance, with λ0 = 8 µm and Ef at 0.3, 0.6 and 0.9 eV, focal lengths of 4.5, 3.8 and 3.5 µm with its corresponding FWHM of 64, 232 and 320 nm, respectively, can be realized. The variation of the focusing efficiency with respect to the incident wavelength and the Fermi level were also investigated. The results of theoretical analysis based on light differential equations agree well with the finite element analysis simulation, which further validate the model.