New insights into the dynamical properties of water in hydroxyapatite (HAP) nanopores, a model system for the fluid flow within nanosize spaces inside the collagen-apatite structure of bone, were obtained from molecular dynamics simulations of liquid water confined between two parallel HAP surfaces of different sizes (20 angstrom <= H <= 240 angstrom). Calculations were conducted using a core-shell interatomic potential for HAP together with the extended simple point charge model for water. This force field gives an activation energy for water diffusion within HAP nanopores that is in excellent agreement with available experimental data. The dynamical properties of water within the HAP nanopores were quantified in terms of the second-order water diffusion tensor. Results indicate that water diffuses anisotropically within the HAP nanopores, with the solvent molecules moving parallel to the surface twice as fast as the perpendicular direction. This unusual dynamic behaviour is linked to the strong polarizing effect of calcium ions, and the synergic interactions between the water molecules in the first hydration layer of HAP with the calcium, hydroxyl, and phosphate ions, which facilitates the flow of water molecules in the directions parallel to the HAP surface.