In this study, a conductive composite material, based on graphene oxide (GO), nanocellulose (CNF), and tannins (TA) from pine bark, reduced using polydopamine (PDA), was developed for wound dressing. The amount of CNF and TA was varied in the composite material, and a complete characterization including SEM, FTIR, XRD, XPS, and TGA was performed. Additionally, the conductivity, mechanical properties, cytotoxicity, and in vitro wound healing of the materials were evaluated. A successful physical interaction between CNF, TA, and GO was achieved. Increasing CNF amount in the composite reduced the thermal properties, surface charge, and conductivity, but its strength, cytotoxicity, and wound healing performance were improved. The TA incorporation slightly reduced the cell viability and migration, which may be associated with the doses used and the extract’s chemical composition. However, the in-vitro-obtained results demonstrated that these composite materials can be suitable for wound healing.