The major principal stress direction angle (ασ) experienced by granular soils varies widely in engineering, causing different strengths. However, how particle morphology affects the strength anisotropy behavior under different ασ remains unclear. To address this gap, this study performed drained hollow cylinder torsional shear tests under different ασ on six granular materials with distinct morphologies. Results highlight the significant dependence of peak strengths of granular materials on both particle morphology and ασ. Increasing particle shape irregularity and surface roughness leads to a considerable enhancement in peak strength, while this peak strength significantly degrades with increasing ασ. Materials with more irregular shapes were found to have a more pronounced strength anisotropy. Furthermore, the initial fabric of particle packings, derived from three-dimensional X-ray microtomography, was used to interpret microscopic mechanisms behind the morphology-dependent strength anisotropy. Irregular-shaped materials display broader preferred particle orientations and higher initial fabric anisotropy compared to relatively regular-shaped materials. This higher morphology-induced fabric anisotropy contributes to strength anisotropy, and a correlation was established for describing this trend. Additionally, an anisotropic failure criterion incorporating fabric anisotropy was developed to characterize the strength envelope for granular materials with diverse shapes.