A model to predict crack initiation life of an additive manufactured nickel-based superalloy similar to Hastelloy X subjected to low-cycle fatigue loading at room temperature has been developed, taking material anisotropy into account. An anisotropic constitutive model based on the Hill yield criterion was developed, with linear kinematic hardening up to a saturation value of the back stress, above which the material behaves perfectly plastic. Low-cycle fatigue experiments has been performed on additive manufactured smooth bars with two different build orientations, with an angle of 0 degrees and 90 degrees relative to the building platform. A total of 20 experiments at room temperature were conducted with different strain ranges and R-values. To predict the crack initiation life of the specimens, a model based on the Smith-Watson-Topper (SWT) parameter has been established, where ten of the specimens were used to calibrate the initiation model, and the remaining specimens were used for validation. Using this model, the obtained crack initiation life agrees well with the experiments.