While electrospinning is an effective technology for producing poly(hydroxybutyrate-co-hydroxyvalerate) (PHBV) micrometre-scale fibrous scaffolds for tissue regeneration, electrospinning of PHBV fibrous scaffolds composed of sub-micrometre fibres, surface-porous fibres or nanocomposite fibres is rarely explored. In this study, the average PHBV fibre diameter was successfully reduced to the sub-micrometre scale by dissolving a conductivity-enhancing salt in the polymer solution for electrospinning. Surface-porous fibres were made using a mixture of solvents, and carbonated hydroxyapatite (CHA) nanoparticles were incorporated into the fibres with the aid of an ultrasonic power source. Water contact angle measurements demonstrated that both fibre diameter reduction and CHA incorporation enhanced the wettability of the fibrous scaffolds. Tensile properties of the scaffolds were not undermined by the reduction of fibre diameter and the presence of surface pores. In vitro biological evaluation using a human osteoblast-like cell line (SaOS-2) demonstrated that all types of fibrous scaffolds supported cell attachment, spreading and proliferation. Analysis of cell morphology revealed similar projected cell areas on all types of scaffolds. However, cells on sub-micrometre fibres possessed a lower cell aspect ratio than cells on microfibres. The reduction of fibre diameter to the sub-micrometre scale enhanced cell proliferation after 14 days cell culture, while the incorporation of CHA nanoparticles in microfibres significantly enhanced the alkaline phosphatase activity of SaOS-2 cells. The control of fibre diameter, surface topography and composition is important in developing electrospun PHBV-based scaffolds for specific tissue-engineering applications.