The aim of this work was to develop novel electrospun nanofiber meshes coated with a biomimetic calcium phosphate (BCP) layer that mimics the extracellular microenvironment found in the human bone structure. Poly (epsilon-caprolactone) (PCL) was selected because of its well-known medical applications, its biodegradability, biocompatibility and its susceptibility to partial hydrolysis by a straightforward alkaline treatment. The deposition of a calcium phosphate layer, similar to the inorganic phase of bone, on PCL nanofiber meshes was achieved by means of a surface modification. This initial surface modification was followed by treatment with solutions containing calcium and phosphate ions. The process was finished by a posterior immersion in a simulated body fluid (SBF) with nearly 1.5 x the inorganic concentration of the human blood plasma ions. After some optimization work, the best conditions were chosen to perform the biological assays. The influence of the bone-like BCP layer on the viability and adhesion, as well as on the proliferation of human osteoblast-like cells, was assessed. It was shown that PCL nanofiber meshes coated with a BCP layer support and enhance the proliferation of osteoblasts for long culture periods. The attractive properties of the coated structures produced in the present work demonstrated that those materials have potential to be used for applications in bone tissue engineering. This is the first time that nanofiber meshes could be coated with a biomimetic bone-like calcium phosphate layer produced in a way that the original mesh architecture can be fully maintained.