FeNiCrCoCu high-entropy alloys (HEAs) have excellent mechanical properties due to high mixing entropy, lattice distortion, sluggish diffusion, and the cocktail effect, so they are widely used in aerospace, energy, machinery manufacturing, and other fields. Experimental studies have revealed that FeNiCrCoCu HEAs exhibit Cu elemental segregation at grain boundaries (GBs); however, the mechanism of Cu segregation on shear deformation at GBs remains unclear. To address this phenomenon, this study adopted a combination of molecular dynamics (MD) simulation and Monte Carlo (MC) simulation to investigate the effect of Cu segregation on GB deformation under shear loading, using Σ11(113) GB as a model system. Initially, the hybrid MC/MD simulation technique was used to generate the models with Cu segregation, and then the cases of random Cu distribution were considered for comparison. The stress-strain curves, dislocation density, and GB behavior under shear loading were analyzed in detail. The results showed that under shear stress, the GB without Cu segregation exhibited GB migration dominated by disconnection nucleation and extension. In contrast, as the degree of Cu segregation at the GB increased, the GB deformation gradually transformed into dislocation emission from the GB, while the required shear strength also increased. Further analysis revealed two reasons for the change in GB behavior. First, the Cu element segregation at the GB changed the chemical environment near the GB, reduced stress concentration at the GB, decreased GB energy and GB free volume, thereby hindering GB migration. Second, the high concentration of Cu elements at the GB region had a pinning effect on the GB, which further impeded GB migration. The inhibitory effect of Cu segregation on GB migration was also observed in Σ5 (210), Σ17 (410), and Σ27 (115) GBs. Overall, this study demonstrates the effect of GB segregation of Cu on the mechanical properties and GB deformation response of FeNiCrCoCu HEAs and highlights the importance of GB composition for tailoring high-strength materials. These findings provide a new perspective for understanding GB behavior of high-entropy alloys and contribute to the design and development of future high-performance alloys.