Various wound dressings have been developed so far for wound healing, but most of them are ineffective in properly reestablishing the skin's structure, which increases infection risks and dehydration. Electrospun membranes are particularly interesting for wound dressing applications because they mimic the extracellular matrix of healthy skin. In this study, a potential wound healing platform capable of inducing synergistic antibacterial and antioxidation activities was developed by incorporating bio-active rosmarinic acid-hydroxyapatite hybrid (HAP-RA) with different contents (0.5, 1, and 1.5 wt.%) into the electrospun polyamide 6 (PA6) nanofibers. Then, polyethylene glycol (PEG) was introduced to the nanofibrous composite to improve the biocompatibility and biodegradability of the dressing. The results indicated that the hydrophilicity, water uptake, biodegradability, and mechanical properties of the obtained PA6/PEG/HAP-RA nanofibrous composite enhanced at 1 wt.% of HAP-RA. The nanofibrous composite had excellent antibacterial activity. The antioxidation potential of the samples was assessed in vitro. The MTT assay performed on the L929 cell line confirmed the positive effects of the nanofibrous scaffold on cell viability and proliferation. According to the results, the PA6/PEG/HAP-RA nanofibrous composite showed the desirable physiochemical and biological properties besides antibacterial and antioxidative capabilities, making it a promising candidate for further studies in wound healing applications.