The achromatic subdiffraction lens with large numerical aperture (NA) is of significant importance in optical imaging, photolithography, spectroscopy, and nanophotonics. However, most of the previous research on subdiffraction lenses has been restricted by limited bandwidth and efficiency as well as severe chromatic aberrations. In this paper, a semicircular gradient index lens (sGRIN) with a modified refractive index profile originated from a Maxwell fish-eye lens is put forward to achieve highly efficient (above 81%) achromatic (4–20 GHz) subdiffraction focusing at the focusing line (around $0.28\lambda$) with large NA of 1.3 and broadband diffraction-limited far-field radiation (4–16 GHz) theoretically, which overcomes the drawbacks of previous works. The presented lens is designed by gradient dielectric metamaterials. Evanescent waves ignited at the lens/air interface and transformation of electromagnetic (EM) waves with high spatial frequency in sGRIN to EM waves with low spatial frequency in air are responsible for subdiffraction focusing and diffraction-limited far-field radiation, respectively. Experimental results demonstrate the excellent performance of achromatic subdiffraction focusing and diffraction-limited far-field radiation. The presented lens has great potential to be applied in subdiffraction imaging systems.