For polycrystalline materials, key material properties, such as mechanical anisotropy or transformation behavior, and magnetic properties strongly depend on the crystallographic texture of the crystalline material. Assessment of texture is generally destructive and highly local. Only high energy X-ray diffraction at synchrotron sources and neutrons enable to study, non-destructively, the microstructure in the bulk of materials. Here, we report how progress in Laue three-dimensional neutron diffraction tomography enables to index the crystallographic orientation of several hundred grains and, thus, enables grain-resolved characterization of texture in the volume of centimeter-sized coarse-grained samples with statistical significance. To demonstrate the neutron technique for characterizing the crystallographic microstructure, we investigate a Fe-Ni-Mn austenitic alloy. A total number of 481 grains within a 1 cm³ of material is indexed and the results in assessing the crystallographic texture are compared with electron backscatter diffraction measurements. The short exposure times and non-destructive nature of the Laue three-dimensional neutron diffraction render it a novel promising method for corresponding characterization.