Design of functionally gradient composite was carried out as a basic study to develop a bio-mimetic composite material. A cross-ply laminate structure, $[0/90/0/core]_{s}$, was considered for a functionally gradient bio-mimetic composite structure that could prevent stress concentration caused by the difference between the elastic moduli of the cortical bone and the artificial hip joint. A cross-ply laminate plate with rectangular cross-section and a beam with circular cross-section were studied before a functionally gradient composite of the actual shape was investigated. Four point bending test was conducted with the wet and dry bovine femur specimens to examine mechanical properties of the cortical bone. The wet and dry bovine femur specimens to examine mechanical properties of the cortical bone. The wet bone showed a non-linear stress-strain relation but the dry bone showed a linear stress-strain relation. Mechanical properties of the proposed functionally gradient composites were calculate as a function of the layer thickness and carbon fiber volume fraction in each layer based on the Halpin-Tsai equation, CLPT(classical laminate plate theory), rule of mixture, and beam theory.