Radial nonsymmetrical fiber endface microlenses original fabrication technique has been used for high efficient pump laser diode radiation coupling (up to 93% without AR coating) into the standard optical fibers and for the form of a pump power diagram at the output fiber endfaces. Nd:GdVO4 laser (2.5 mm crystals length) parameters with semiconfocal (output mirror curvature radius 10 cm) and monolith plane mirrors cavities have been measured for different pump diagrams formed by plane endfaces, spherical microlenses, and Selfoc lenses. Compact diode-pumped solid state lasers may be used in optical communications, optical storage, medicine, and other applications. Diode laser (DL)-optical fiber coupling gives several advantages for these pumping systems -- a possibility to combine several DLs radiation, a remote DLs mounting, small size and electrical safety of the laser heads, simple schemes of active crystals cooling, axial symmetry of the pumping beam for longitudinal geometry. In general, high coupling efficiency between a semiconductor light source and optical fiber may be achieved by the use of microlens, formed on the endface of the fiber. In this case bulk optical components between DL and optical fiber are not needed. In addition, the only reflection surface exists in this coupling technique. Different techniques for producing microlenses on a fiber endface have been developed. For example, tapered hemispherical lenses, melted, etched, and polished lenses are commonly used for this coupling. However, all types of such techniques produce in general radial symmetry lenses: therefore, they do not provide efficient coupling between a round fiber core and a nonsymmetrical DL's radiation. In this paper we demonstrate the fabrication technique of fiber endface radial nonsymmetrical microlenses with radii curvature from few micrometers to few tens micrometers by grinding/polishing process. This process may be used for producing different nonspherical microlenses (cylindrical, elliptical, hyperbolic, etc.) to efficient coupling DL's radiation into single-mode or multimode optical fibers and for producing microlenses (including spherical) on the output fiber endface to form a diagram of a pumping power.