Biomimetic mineralization of high-strength apatite structure essentially relies on mimicking the inorganic building blocks of naturally occurring bones. However, conventional routes still have substantial function gaps in providing precision control over the geometrical dimensions and crystalline morphology of biomineralized apatite. Herein, we conceived the concept of microwave-assisted biomineralization (MAB) to customize 1D hydroxyapatite nanowhiskers (HANWs) at graphene templates, rendering the formation of graphene-hydroxyapatite (Gr-HA) nanohybrids. The HANWs essentially resembled bone apatite in elemental composition (Ca/P = 1.74), diameter (~20 nm), crystallinity (63 %), and rodlike geometry (aspect ratio of ~6). The Gr-HA nanohybrids were uniformly incorporated into poly(lactic acid) (PLA) microfibers (~1 μm) by electrospinning, engendering fibrous membranes with a set of Gr-HA loadings (10, 20 and 30 wt%). Intimate interactions were generated between Gr-HA and PLA matrix, contributing to significant promotion of the mechanical properties for PLA composite membranes. For example, the yield strength and elastic modulus of the PLA composite membranes loaded with 30 wt% Gr-HA achieved 5.4 and 66.4 MPa, increasing nearly 182 % and over 94 % compared to those of pure PLA, respectively. Moreover, the bone-like HANWs endowed PLA membranes with excellent cytocompatibility and good bioactivity, as demonstrated by over 38 % increase in cell viability and rapid apatite formation in mineral solution. The impressive combination of mechanical properties and biological characteristics make the PLA/Gr-HA scaffolds promising for guided tissue/bone regeneration therapy. The concept of microwave-assisted biomineralization was conceived to customize 20-nm-sized hydroxyapatite nanowhiskers with bone apatite-like structural features, conferring a combination of mechanical strength, osteogenesis and bioactivity for the poly(lactic acid) scaffolds. Display omitted •A microwave-assisted biomineralization (MAB) approach was established.•MAB enabled rapid fabrication of hydroxyapatite nanowhiskers (HANWs) at graphene templates.•The HANWs (diameter of ~20 nm, crystallinity of 63 %) copied the structure of bone apatite.•The bone-like HANWs promoted the osteogenesis and bioactivity of poly(lactic acid) scaffolds.