As a natural biopolymer, sodium alginate (SA) has been widely used in the biomedical field in the form of powder, liquid, gel, and compact solid, but not in the form of nanofiber. Electrospinning is an effective method to fabricate nanofibers. However, electrospinning of SA from its aqueous solution is still a challenge. In this study, an effort has been made to solve this problem and find the key reasons that hinder the electrospinning of alginate aqueous solution. Through this research, it was found that pure SA nanofibers could be fabricated successfully by introducing a strong polar cosolvent, glycerol, into the SA aqueous solutions. The study on the properties of the modified SA solution showed that increasing glycerol content increased the viscosity of the SA solution greatly and, meanwhile, decreased the surface tension and the conductivity of the SA solution. The theological results indicated that the increase in glycerol content could result in the enhanced entanglements of SA chains. Two schematic molecular models were proposed to depict the change of SA chain conformation in aqueous solution with and without glycerol. The main contribution of glycerol to the electrospinning process is to improve the flexibility and entanglement of SA chains by disrupting the strong inter- and intramolecular hydrogen bondings among SA chains, then forming new hydrogen bondings with SA chains.