In this paper a 3D-topology optimization method in electromagnetism is introduced to design 3D-magnetic circuits. Some new theoretical results are provided to deal with 3D design cases in order to compute the derivatives using the adjoint method. Moreover, an homothopy algorithmic optimization approach is developed based on SIMP to enforce the convergence to discrete solutions close to be manufacturable. This new approach is applied and validated to design a 3D-magnetic circuit with close to 20000 variables.