Compared with other 3D printing methods, binder jet 3D printing (BJ3DP) shows the great potential for obtaining large-scale complex parts with high efficiency and low cost. However, understanding the sintering behavior of powders is one of the challenging topics in BJ3DP. In this work, on the basis of the thermo–elasto–viscoplastic constitutive law model, the sintering behavior of 316 L stainless steel (316 L SS) cuboids prepared by BJ3DP with different initial relative densities (relative densities of green parts), i.e., 49.5%, 51.5% and 53.5%, was investigated via finite-element numerical simulations. It suggested that the shrinkage decreased as the initial relative density increased, resulting from that a higher initial relative density would provide higher sintering stress. Additionally, precise shrinkage and final relative densities of the BJ3DP samples were quantitatively predicted via numerical simulations, and the simulated results were in good agreement with experimental results. According to the experimental results, a final relative density of ~98.7% could be achieved in the BJ3DP 316 L SS sample with an initial relative density of 53.5% after sintering, showing a yield strength of ~308 MPa and an ultimate tensile strength of ~601 MPa along with a total elongation of ~59.4%.