Calcium carbonate (CaCO3) fibers were prepared by electrospinning followed by annealing. Solutions consisting of calcium nitrate tetrahydrate (Ca(NO3)2·4H2O) and polyvinylpyrrolidone (PVP) dissolved in ethanol or 2-methoxyethanol were used for the fiber preparation. By varying the precursor concentrations in the electrospinning solutions CaCO3 fibers with average diameters from 140 to 290 nm were obtained. After calcination the fibers were identified as calcite by X-ray diffraction (XRD). The calcination process was studied in detail with high temperature X-ray diffraction (HTXRD) and thermogravimetric analysis (TGA). The initially weak fiber-to-substrate adhesion was improved by adding a strengthening CaCO3 layer by spin or dip coating Ca(NO3)2/PVP precursor solution on the CaCO3 fibers followed by annealing of the gel formed inside the fiber layer. The CaCO3 fibers were converted to nanocrystalline hydroxyapatite (HA) fibers by treatment in a dilute phosphate solution. The resulting hydroxyapatite had a plate-like crystal structure with resemblance to bone mineral. The calcium carbonate and hydroxyapatite fibers are interesting materials for bone scaffolds and bioactive coatings.