This work introduces a computational method for designing bone scaffolds for maximum bone growth. A mechanobiological model of bone adaptation is used to compute the bone growth, taking into account the shape of the defect, the applied loading, and the existing density distribution of the bone in which the scaffold has been implanted. Numerical homogenization and a geometry projection technique are used to efficiently obtain surrogates of the effective elastic and diffusive properties of the scaffold as a function of the scaffold design and the bone density. These property surrogates are in turn used to perform bone adaptation simulations of the scaffold-bone system for a sampling of scaffold designs. Surrogates of the bone growth in the scaffold at the end of the simulated time and of the strain energy of the scaffold at implantation time are subsequently constructed from these simulations. Using these surrogates, we optimize the design of a scaffold implanted in a rabbit femur to maximize bone growth into the scaffold while ensuring a minimum stiffness at implantation. The results of the optimization demonstrate the effectiveness of the proposed design methodology and they provide evidence that designing a scaffold with regards to bone adaptation yields larger bone growth than considering only mechanical criteria.