A living tissue-engineered skin graft having a potential to develop hair follicles includes a multilayered skin-like structure of alternating nanofiber mats and layers of fibroblasts assembled in a layer-by-layer fashion. Aggregates of dermal papilla capable of developing into hair follicles are embedded in the multilayered structure such that the aggregates develop into hair follicles upon culturing the multilayered structure. Keratinocytes are provided as an outer layer of the skin graft. Fibroblasts, keratinocytes and dermal papilla cells are isolated from skin and cultured to form suspensions of cells for fabricating the skin graft. Aggregates of dermal papilla cells are generated using a hanging drop method. Nanofiber mats are formed by electrospinning biocompatible materials onto a culture media or a layer of fibroblast suspension. The skin graft has dermal and epidermal layers and provides a biomimetic environment to promote healing and hair growth.