The article presents a new methodology that employs 3D printing technology to generate a microporous composite material of polylactic acid, sodium alginate and hydroxyapatite, whose microstructure is designed by means of the 3D numerical solution from a mathematical model. This model represents the spatio-temporal dynamics of the interaction between osteoblasts and osteoclasts in the bone remodeling. The microporosity of composite material mimics the structure of human trabecular bone. This material has density with microporosity pretty close to the one that is exhibited by the natural bone tissue. Close relationship between the material processing and its elasticity module is observed. When subjecting this composite material to a simulated body fluid treatment, the mechanical resistance to compression is increased due to induced mineralization of hydroxyapatite crystals on its surface. The methodology shows potential to generate structures that allow the control of the composite material properties. The material presents a microporosity that has morphological and chemical properties suitable for future applications in tissue engineering as bone scaffold.