Residual stresses are a serious complication in additive manufacturing (AM), especially for producing large metallic components. These residual stresses are caused by the large thermal gradients and phase transformations during the manufacturing process. Too large residual stresses can result in cracks in the workpiece or detachment from the baseplate, as well as considerable distortion during and after fabrication. The recently proposed space-time topology optimization enables simultaneous optimization of the structural layout and the fabrication sequence [1]. It is motivated by the fact that the performances of additively manufactured components depend on both the structural design and the process planning. In addition to a pseudo-density field for representing the structural layout, space-time topology optimization introduces a pseudo-time field to encode the fabrication sequence. In this paper, we demonstrate the feasibility of reducing residual stresses in AM by using space-time topology optimization. An anisotropic inherent strain method is adopted as a simplified process simulation model to predict the residual stress accumulation. The anisotropic inelastic strain field is aligned with the curved layers, which is derived from the gradient of the pseudo-time field [2]. Afterwards, the local residual stresses are aggregated into a global constraint using the p-mean function. This stress-constrained space-time topology optimization framework is parallelizable, and we implement it using PETSc for computational efficiency. Numerical examples show that optimizing fabrication sequence provides an extra dimension to reduce residual stresses during manufacturing. Furthermore, space-time topology optimization allows us to design high performance components with restricted residual stresses.