Technical limitations of traditional electrospinning make it hard to produce three-dimensional (3D) scaffolds with hierarchical pore structures. Here, porous polycaprolactone (PCL) nanofiber meshes with different nano-hydroxyapatite (nHA) concentrations were prepared by electrospinning with stainless steel mesh as the collector, and 3D porous nanofiber scaffolds were fabricated via layer-by-layer assembly with a special binder (18% PCL/DCM solution). The single layer nanofiber mesh possessed very regular morphology with a hollow structure, and the nHA was not only embedded in the nanofiber but also exposed on the surfaces of the fiber, resulting in the improved surface chemical properties. The incorporation of nHA also had a significant effect on cell behaviours and functions. The 3D nanofiber scaffolds possessed hierarchical structures with interconnected micro and macro pores, which allowed cells to migrate between the adjacent layers, even throughout the scaffold. Cells filled the scaffold space and integrated with the nanofiber materials, forming scaffold/cells complexes in vitro. In addition, alendronate was successfully carried on the 3D composite scaffolds because of the high affinity of P–C–P backbone to calcium ions. The composite scaffolds treated with alendronate significantly promote the osteogenesis-related gene expression of human foetal osteoblasts. All these results suggest that 3D functional nanofiber scaffolds would be potentially useful for bone repair.