In this study, the formation of conductive nano-structured polypyrrole (PPy) on electrospun poly(ɛ-caprolactone) (PCL) nanofibers was successfully achieved using a DNA dopant (PCL/DNA-PPy) via sonication-induced layer-by-layer assembly. After PPy containing positive charges was accumulated on PCL, DNAs with negative charges deposited such that they were evenly distributed. The resulting PCL/DNA-PPy nanomembrane exhibited increased fiber diameter (PCL/DNA-PPy 5LBL: 328.11 ± 48 nm) and deformation morphology compared to pure PCL (average fiber diameter of 247.25 ± 32 nm, fibrous uniform morphology), as observed using scanning electron microscopy and atomic force microscopy. As the number of layers increased, the crystallinity of PCL/DNA–PPy nanomembranes decreased, as observed using X-ray diffraction. It was observed that the PPy-DNA deposited on the surface of PCL connected to form a nano-sheath and significantly increased the thermal stability of PCL. Moreover, the contact angle of the PCL/DNA-PPy nanomembrane (contact angle of pure PCL: 79.3 ± 1.2°) demonstrated its high hydrophilicity. The results indicate that the composites showed very good survival in a cytotoxicity test on U-118 glioma cells and excellent electrical conductivity (the highest value was 1.1 × 10−3 S/m). The manufactured PCL/DNA–PPy nanomembranes are considered to be promising materials for applications in the scaffold, sensor, and electronic fields.