To study two-phase flows occurring in the process of coaxially electrospinning core-shell composite nanofibers, a mathematic physical model was proposed with shear-thinning fluid properties, surface tension, and electric fields specially considered. Numerical results showed three flow patterns: slug, slug-annular transitional, and annular flows. According to a flow pattern model based on the Weber number, slug-annular transitional flows were predicted to occur when the Weber number was between 0.5 and 26, whereas the slug and annular flows were to be expected when the Weber number was less than 0.5 and greater than 26, respectively. Body forces (induced by electric fields) and surface tension forces had more explicit effects on the flow patterns than forces due to viscosity and permeability gradients on interfaces. To form an annular flow pattern with smooth core-shell interfaces, which is favored in engineering practice, the applied electric field should be stronger than 100 kv/m.