Bone remodeling is the process of ongoing replacement of old bone by new. The remodeling process is achieved by bone-resorbing osteoclasts and bone-forming osteoblasts. In terrestrial vertebrates, activities of these two types of cells are strictly balanced and adapt the shape of bone to mechanical stress. A simple bone remodeling model by coupling the bone formation and resorption based on Turing reaction-diffusion system weighed by local mechanical stress was proposed. This model was coupled with finite element method by using the element adding and removing process, and a new bionic topology optimization model was established. The major idea of this approach is to consider the continuum structure to be optimized as a piece of bone, and the process of finding the optimum topology of a structure was equivalent to the bone remodeling process. Uniform distribution of strain-energy density as a guideline updated the material distribution, until equilibrium was reached and then the optimal topology structure was obtained. The effectiveness of the present method is demonstrated by some numerical examples.