We present the design, fabrication, and experimental measurements of an Axial Gradient-index (AGRIN) flat lens synthesized by 2D periodic metallic patches on a grounded dielectric slab, known as metasurfaces. Metasurfaces can be considered as artificial materials that possess unique characteristics, which mainly revolve around the two-dimensional distribution of the structure. By manipulating the phase and amplitude of the near-fields over the surface of the metasurface, specific values of the effective permittivity and permeability can be achieved, thereby regulating the overall field behavior by gaining control of the refractive index that is related to the aforementioned two material parameters. By configuring the refractive index, metasurfaces enable the manipulation of the direction in which electromagnetic waves propagate, as dictated by Snell's law. By varying the geometric dimensions of unit cells in each segment that compose the lens, the gradient refractive index profile required for our AGRIN lens can be achieved. A primary feature of this lens lies with its semicircular structure, in contrast to conventional circular ones. Its perimeter comprises a convex boundary and a straight one. In comparison to traditional circular lenses like the Luneburg lens and Maxwell fisheye lens, our proposed AGRIN lens offers the advantage of being more compact. Despite its smaller area, the AGRIN lens maintains its focusing ability. The AGRIN lens is capable of focusing over 71.75% of the energy from the incident wave onto the focal point. This efficient focusing ability, combined with its reduced size, makes the AGRIN lens highly advantageous for various applications.