The work studied the effect of structuring of gelatin solution with a different content of acetic acid on the stability of electrospinning process and obtained nanofibers morphology. Using the method of dynamic light scattering and analysis using the Arrhenius equation, it was found that the process of formation of gelatin sol is thermally activated, and the activation energy of the process increases from 70.2 to 102.2 kJ/mol with the introduction of 10 vol.% acetic acid. Using dynamic mechanical analysis of viscoelastic properties, it was found that when the solution concentration is more than 15 wt.% in the presence of 10 vol.% acid, a structure of the solution close to a gel is formed. It has also been shown that as the fraction of acid increases to 25 vol.% and higher solutions are characterized by a sol state with an increase in the elastic component after 24 h of solution settling. It was found that the structuring of the solution during settling affects the stability of electrospinning. Statistical analysis of the morphology of gelatin nanofibers showed that with an acid content of 25 vol.% the average diameter of nanofibers increases by 2 times during settling of 24 h. When using an acetic acid content in a gelatin solution of more than 50 vol.%, a significant increase in the stability of the electrospinning process and in the average diameter of nanofibers were observed, regardless of the settling time.