Super-resolution lenses (SRLs) based on the principle of optical super-oscillation are composed of subwavelength structural units, which can achieve precise control of light properties through suitable design. A bio-inspired SRL structure with Fermat Spiral-arranged dielectric nano-column is proposed in this paper for the first time. Owing to the unequally spaced arrangement of the Fermat Spiral, the proposed SRL can effectively suppress the sidelobe of the focal field and achieve a high focusing efficiency. The focusing properties of the SRL are investigated detailedly by simulation. The focusing efficiency and the peak sidelobe ratio of the focal field are 72.8% and 16.02 dB, respectively, at the wavelength of 1.55 μm. And an ultra-wide working bandwidth of 200 nm are achieved by the proposed SRL with high focusing efficiencies and low sidelobe energies in the whole bandwidth. In addition, the sub-diffraction limit focusing is achieved by only controlling the radius of the nano-columns, and the bio-inspired Fermat Spiral-arranged SRL exhibits a large tolerance of the fabrication error.