The fast and precise fabrication of three-dimensional (3-D) structures made of nanofibers is an important development trend in the electrospinning technique. This paper describes a new and facile method of electrospinning to fabricate nanofibrous 3-D structures. The nanofibrous 3-D structures can be engineered to have the desired layer thicknesses, where the fiber spacing, density (i.e., fiber volume/unit volume), as well as shape of the structure may be controlled. While innumerable structural variations are possible with this method, this paper discusses, as proof-of-concept, a few cases that illustrate how 3-D nanofiber webs can be made for filtration application. Computerized automation of the method will make it possible to build almost any 3-D web structure suitable for a myriad of applications including ultra-light-weight insulation and scaffolds for hydrogel preparation and tissue.