FeCrMnxAlCu (x = 2.0, 1.5, 1.0, 0.5, and 0.0) high-entropy alloys (HEAs) were prepared using vacuum arc melting. The phase structure, microstructure, and element distribution of FeCrMnxAlCu (x = 2.0, 1.5, 1.0, 0.5, and 0.0) HEAs were analyzed using X-ray diffraction, scanning electron microscopy, and energy-dispersive spectroscopy. The corrosion resistance of the alloy in a NaOH solution was evaluated using a potentiodynamic polarization curve, electrochemical impedance spectroscopy, an immersion test, WLI, and X-ray photoelectron spectroscopy. The results showed that FeCrMnxAlCu HEAs are an FCC+BCC bi-phase mixed structure with typical dendrite and interdendrite structures. The corrosion test demonstrated that the HEAs presented a breakthrough characteristic of activation–passivation–passivation. With an increase in Mn content, the corrosion potential shifted first positively and then negatively, and the corrosion current first decreased and then increased. Among HEAs, the FeCrMn0.5AlCu HEA had the best electrochemical corrosion resistance. After corrosion, both oxide and hydroxide corrosion product films were formed on the surface, which reduced the ion diffusion rate, slowed down the corrosion process, and improved the corrosion resistance.