In this study, we successfully fabricated a novel drug and plasmid DNA (pDNA) dual delivery system by electrospinning the dispersion composed of polyethyleneimine-carboxymethyl chitosan/pDNA-angiogenin (ANG) nanoparticles, curcumin (Cur), poly (D, L-lactic-co-glycolic acid) (PLGA), and cellulose nanocrystals (CNCs). In vitro release studies showed that the bioactivity of Cur and ANG was preserved in the nanofibers, and a sequential release pattern was achieved in which nearly 90% of the Cur was released in ca. 6 days and the ANG release lasted up to about 20 days. In vitro cell culture results suggested that the composite nanofibers exhibit excellent biocompatibility. To evaluate the in vivo angiogenesis and anti-infection properties, the PLGA/CNC/Cur/pDNA-ANG composite nanofibers were transplanted into the infected full-thickness burn wounds. Biopsy specimens were harvested for histology, immunohistochemistry, immunofluorescence, real-time quantitative PCR, and Western blotting analyses. The results indicated that the PLGA/CNC/Cur/pDNA-ANG composite nanofibers not only prevented local infection but also promoted skin regeneration.