The tensile and fatigue properties of laser-powder-bed-fusion (L-PBF) processed Ti-6Al-4V specimens are investigated at different loading conditions. Two types of as-built and post-machined L-PBF processed dogbone specimens are considered for the study, one is an ASTME8M round specimen and the other one is a customized small-scale flat structure. The tensile and fatigue behavior of the specimens are investigated numerically using the finite element (FE) method. The FE modeling considers both low cycle fatigue (LCF) and high cycle fatigue (HCF) test conditions by applying cyclic loads in fully-reversed and stress ratio R = 0.1 conditions. The FE results for the von Mises stress, strain, total deformation, fatigue life, factor of safety, and fatigue limit of the Ti-6Al-4V specimens are obtained at room temperature (295 K). Results obtained from the model show that the fatigue life decreases as the load increases. It is also found that fatigue life does not vary with the change of the test frequency under a specific fatigue load. The comparison of mechanical properties of the L-PBF processed specimens with conventionally manufactured Ti-6Al-4V parts is also shown to understand the differences in the tensile and fatigue behavior. The validation of the FE model is performed by comparing the numerical results for the yield stress and fatigue limit with the experimental results found from the literature. The overall study contains a detailed analysis of the tensile and fatigue behavior of additively manufactured Ti-6Al-4V parts and provides a guide to investigating the similar properties for other functional materials used in the L-PBF process.