In the framework of the level-set method we propose a topology optimization algorithm for linear elastic structures which can exhibit fractures. In the spirit of Grith theory, brittle fracture is modeled by the Francfort-Marigo energy model, with its Ambrosio-Tortorelli regularization, which can also be viewed as a gradient damage model. This quasi-static and irreversible gradient damage model is approximated using penalization to make it amenable to shape-dierentiation. The shape derivative is determined using the adjoint method. The shape optimization is implemented numerically using a level-set method with body-tted remeshing, which captures shapes exactly while allowing for topology changes. The eciency of the proposed method is demonstrated numerically on 2D and 3D test cases. The method is shown to be ecient in conceiving crack-free structures.