We employ atomistic computer simulations to study the structure and migration behavior of a Σ11 symmetrical tilt grain boundary in a 4-component model FCC high-entropy alloy (HEA) (CuNiCoFe). The results are compared to grain boundaries in elemental metals and a so-called ‘average-atom’ sample. We find that the repeating structural units characterizing the static grain boundary structure show the same repeating structural units for all samples, while the high temperature equilibrium grain boundary structure is most strongly influenced by presence of stacking faults. Under an applied synthetic driving force, this GB migrates by a mechanism assisted by partial dislocations in all materials. For this reason the grain boundary mobilities and stacking fault energies are directly related. Moreover, the HEA sample and the average-atom sample show almost identical mobilities suggesting that local chemical fluctuations play a minor role. Solute segregation to the GB in the HEA suppresses GB migration up to very high temperatures and might be the main cause for reduced grain growth in FCC HEAs.