Welding and relevant studies are indispensable to employ high-entropy alloys for practical applications. In this study, Al CoCrCu FeNi high-entropy alloy with single FCC phase was used to make “bead-on-plate” friction stir welds at different rotational speeds, and the effects on microstructure and mechanical properties were studied. Several banded structures containing oxide or nitride particles were observed in the stir zone (SZ), and the chemical wear of the polycrystalline cubic boron nitride tool was confirmed. The microhardness distribution of the welds showed higher hardness in the SZ because of grain refinement and the presence of deformed grains. The electron backscattered diffraction results suggested that the high-entropy alloy with low stacking-fault energy experienced recrystallization during friction stir welding, which was similar to other conventional materials with low stacking-fault energy.