A Fe-free Al56-xCo24Cr20Nix (x = 34, 36, 38, 40, and42, denoted as Nix alloys hereafter) eutectic high-entropy alloys were designed and prepared to investigate the effect of Al and Ni content on the microstructure and mechanical property. It was found that all five alloys exhibited a typical eutectic microstructure and an ordered FCC/BCT phase structure, and the volume fraction of BCT phase reduced with an increase in Ni content. The FCC and BCT phases were enriched in Cr-Co and Al-Ni elements respectively, and the nano-scale precipitates forming in BCT phase also exhibited a BCT phase structure but enriched in Cr element. The Ni38 alloy displayed an entire eutectic microstructure with two types of eutectic lamellas, the long and straight one, and the short and curve one. The irregular lamellas resulted in an unsatisfactory tensile property in Ni38 alloy with a yield strength of 543 MPa and a fracture strain of 8.1 %. To optimize the strength-plasticity configuration, the Ni content was further fine-turned. The Ni38.5 alloy, exhibiting a regularly and fine lamellar hypereutectic microstructure with bits of primary FCC phase, was found presenting an improved fracture strain of 14.5 % and without any reduction in yield strength compared with Ni38 alloy.