The nonlinear small strain shear stiffness of soil is widely acknowledged to vary significantly under different stress paths by experimental studies. However, the mechanism related to the path-dependent small strain stiffness of granular materials has not been well understood. This study adopted the discrete element method (DEM) to investigate the nonlinear shear stiffness reduction curves of Fujian sand. Several typical stress paths were examined in DEM simulations, corresponding to stress path rotation angles of 0°, 90°, -90°, and 180°. The Hertz-Mindlin contact model was employed, and microscopic parameters such as particle shear modulus (Gg) and inter-particle friction coefficient (μ) were calibrated to achieve good agreement between DEM and experimental results. The results indicate that the normalized stiffness reduction curve decays more rapidly with increasing Gg, while it decreases more slowly with increasing μ. With the calibrated parameters, DEM using Hertz-Mindlin contact model can both qualitatively and quantitatively capture the effect of stress path on the nonlinear stiffness of granular materials, providing a valuable basis for further exploration within micro scale.