In order to explore the effect of rare earth elements (REEs) on the eutectic high-entropy alloys (EHEAs), 0.2 atomic per cent of Sc, Y, and La elements were added to the AlCoCrFeNi2.1(REE0) EHEA in this work. The phase composition, element distribution, electrochemical properties and mechanical properties of the alloys were analysed. The results showed that the AlCoCrFeNi2.1-based HEAs are still composed of Co, Cr, Fe (face-centred cubic)-rich phase and Al, Ni (face-centred cubic)-rich phase. After Sc, Y, La were added, Ni2Sc, Al2Y, Al2La and other intermetallics were formed in the AlCoCrFeNi2.1 alloy. In addition, it was proved that Y element can promote the formation of hexagonal close-packed (HCP) phase. AlCoCrFeNi2.1Y0.2(Y0.2) alloy has excellent corrosion resistance. AlCoCrFeNi2.1Sc0.2(Sc0.2) alloy has the best mechanical properties. HIGHLIGHTS With the addition of rare earth elements, the face-centred cubic phase and the B2 phase still exist in the alloy. In addition, there are intermetallics in the alloys. Combined with first-principles calculations, it was determined that the Laves phases in AlCoCrFeNi2.1Y0.2 alloy may be Al2Y, Al3Y or AlY. The Laves phase in the AlCoCrFeNi2.1La0.2 alloy may be Al2La, Al3La or LaNi5. The addition of Y element can promote the formation of HCP phase in AlCoCrFeNi2.1 alloy. The generated HCP phase occupies the position of the original B2 phase. Y element can also improve corrosion resistance. The Vickers hardness of AlCoCrFeNi2.1Sc0.2 alloy is 20% higher than that of AlCoCrFeNi2.1 alloy, while the compressive strength of 1897 MPa and the compressive deformation of 26% are retained.