The advanced development of additive manufacturing (AM) has greatly promoted the research and application of variable density porous structures. Meanwhile, AM constraints highlight the significance of design for AM (DFAM). The structural performance of existing topology optimization (TO) based design methods is limited and AM constraints are little considered. In this paper, we propose a novel optimization design method of AM oriented porous structures which allows the existence of void. A novel density filter is designed to achieve multi-interval TO for better structural performance and satisfy the minimum feature size constraint. Meanwhile, another customized density filter is designed to obtained support-free porous structure for the buildability constraint of AM. FEA results demonstrate that optimized porous structure designed by proposed method has better stiffness performance and adaptability to AM constraints, compared with existing methods.