Metal additive manufacturing (AM) has been gradually accepted by the industry for manufacturing complex functional end-use components. While metal AM processes are increasingly being adopted, the most critical issue the industry encounters now is build failures resulting from residual stress and distortion induced by the laser process. To address these issues, a novel methodology is proposed to optimize the design of support structure, in order to reduce residual stress and ensure manufacturability. First, a modified inherent strain method is proposed and employed for fast prediction of stress and deformation. It is based on thermomechanical modeling at mesoscale and implemented as a one-time static mechanical analysis. In this manner, process simulation can be significantly accelerated and compatible with structural design. Second, lattice structure constrained stress topology optimization, coupled with fast process simulation, is performed to design the support structure. This not only can prevent build failure by limiting the residual stress to below the yield strength, but also reduce material consumption to build the support structure. Further, the self-support nature of lattice structure makes it ideal for support structure design. Once the density profile of support structure is obtained, a reconstruction scheme is employed to realize the variable density lattice structure for practical application. Several examples are used to demonstrate the effectiveness of the proposed algorithm. Both numerical simulation and experiments show that the proposed method can significantly reduce residual stress and ensure successful printing.