<p>The nonlocal continuum mechanics theory effectively incorporates scale effects and microstructural characteristics of materials into macroscopic mechanical properties, addressing the coupling between macro- and microscale phenomena. Despite its advantages, current computational methods for solving nonlocal elasticity problems face significant challenges: The original volume integral formulation is mathematically complex, while the equivalent differential form still presents numerical difficulties, particularly for complex geometries and boundary conditions in nanoscale structures. This study proposes a novel finite element-differential quadrature (FE-DQ) hybrid method for analyzing the buckling behavior of graphene-equivalent nanoplates. The method combines the geometric flexibility of finite elements with the high-order accuracy of differential quadrature, overcoming limitations of existing approaches. Through comprehensive validation against established results, we demonstrate the method's accuracy and efficiency. Based on the obtained results, the effects of size, nonlocal parameters, and biaxial load ratios on the nonlocal behavior of buckling loads were investigated. The findings indicate that the nonlocal effects on buckling loads decrease with increasing size, while they intensify with higher nonlocal parameters. In contrast, the biaxial load ratio exhibits negligible influence on the nonlocal effects of buckling loads. These results not only validate the effectiveness of the proposed FE-DQ method for nanoscale structural analysis but also provide valuable insights for the design and application of graphene-based nanostructures in flexible electronics, sensors, and nanocomposite materials.</p>