Polymeric fibers enriched with single-walled carbon nanotubes (SWCNT) are known as promising candidates for many applications in textile composites. In these applications, the fiber flexibility, toughness, as well as the fiber conductivity are important parameters. Ideally, one intends to make a fiber which would consist of an interwoven structure of nanotubes and polymer chains. This would make the fibers unique and distinguishable from ally composite materials where the reinforcing elements are incorporated into a polymer matrix forming islands-in-a-sea-type structures. In popular method of fiber spinning based on injection of SWCNT dispersion into polymeric coagulation bath, the concentration of SWCNTs in the fibers is very difficult to control, and, typically, the polymer/SWCNT composition is unknown. As ail alternative to this approach, we propose a new method based on conventional wet spinning technique. The idea is to exploit electrostatic assembling of SWCNTs coated with Sodium Dodecyl Sulfate (SDS). Many polymers important for applications, for example, alginate, chitosan, and polyacrylamide crosslink by ionic crosslinkers. Hence, if one manages to introduce SWCNTs-SDS into the network of these polymers, the resulting material is expected to be very strong and functional. We report oil successful spinning of alginate fibers with carbon nanotube loading as high as 23 wt %. The Young's modulus increases up to 6.38 GPa at 23 wt % SWCNT loading. A transition from a composite structure (discrete SWCNTs embedded in alginate matrix) to a two-component polymer structure (SWCNTs incorporated into Alginate macromolecular network) is discussed using the results of mechanical and morphological characterizations.