We present both a theoretical and an experimental study of a novel compact lensed fiber system utilizing a nanostructured GRIN lens. The lens can be integrated with an optical fiber, which ensures a unique and efficient focusing in any high index medium, such as a liquid. We use the effective medium approach to design lenses with arbitrary refractive index. To fabricate lenses, we utilize a discrete array of nano-sized rods made of two types of glasses, and apply a standard stack-and-draw fiber drawing technology. The fabricated nanostructured GRIN lenses have a parabolic refractive index profile with a diameter of a standard fiber, very short working distances (55 µm in the air) and a high numerical aperture (NA = 0.16). As a proof-of-concept of the new micro-lensed fiber system, we demonstrate an experiment on optical trapping of micrometer-sized glass beads. We also show that our method is compatible with optical fiber technology and allows for any shape of the refractive index distribution in 2D. Thanks to that a new functionality could be achieved by replacing the GRIN lens with an axicon lens, vortex type elements, micro-lenses arrays or diffraction elements.