A modified coaxial electrospinning process was developed for creating drug-loaded composite nanofibers. Using a mixed solvent of ethanol and N,N-dimethylacetamide as a sheath fluid, the electrospinning of a codissolving solution of diclofenac sodium (DS) and Eudragit L100 (EL100) could run smoothly and continuously without any clogging. A series of analyses were undertaken to characterize the resultant nanofibers from both the modified coaxial process and a one-fluid electrospinning in terms of their morphology, physical form of the components, and their functional performance. Compared with those from the one-fluid electrospinning, the DS-loaded EL100 fibers from the modified coaxial process were rounder and smoother and possessed higher quality in terms of diameter and distribution with the DS existing in the EL100 matrix in an amorphous state; they also provided a better colon-targeted sustained drug release profile with a longer release time period. The modified coaxial process not only can smooth the electrospinning process to prevent clogging of spinneret, but also is a useful tool to tailor the shape of electrospun nanofibers and thus endow them improved functions.