In this paper, the fracture behaviors of 316L stainless steel with defects fabricated by the Selective Laser Melting (SLM) additive manufacturing are studied by a peridynamic method. Firstly, the incremental formulations in the peridynamic framework are presented for the elastic-plastic problems. Then, the pairwise force of a bond for orthotropic material model is proposed according to both the local and the global coordinate systems. A simple three-step approach is developed to describe the void defects that generated in the processing of the SLM additive manufacturing in the numerical model. Next, some representative numerical examples are carried out, whose results explain the validation and accuracy of the present method, and demonstrate that the orthotropic features, micro-cracks and voids of the materials have a significant influence on the ultimate bearing capacity, crack propagation and branching of the corresponding structures. It is also revealed that the crack initiations are induced actively by the defects and the crack branching is contributed to the complex multiple-crack propagation. Finally, the achievements of this paper lay a foundation for the engineering applications of the SLM additive manufacturing materials.