Poor fluidity and castability, as well as the compositional inhomogeneity, seriously restrict the industrial production and application of high-entropy alloys (HEAs). To overcome this dilemma, the concept of eutectic HEAs (EHEAs) was proposed, which provides a constructive guide for the alloy design of high-performance HEAs. In this work, the microstructure of HEAs can be controlled by compositional design and a series of eutectic and near-eutectic Ni66-xFe28AlxV6 (x = 16, 17, 18 at%) HEAs can be obtained by adjusting the ratio of Ni to Al content. The microstructure of the designed HEAs transforms from hypoeutectic structure (FCC-primary phase + eutectic structure) to eutectic structure (FCC lamellar + B2 lamellar) and then to hypereutectic structure (B2-primary phase + eutectic structure) with the increasing of Al content from 16 to 18 at%. Thus, the dual-phase eutectic structure comprising of alternating soft FCC/L12 and hard B2 nanolamellae was achieved in the designed Ni49Fe28Al17V6 HEA. The dual-phase orientation relationship of FCC/L12 and B2 interface is determined to be the Kurdjumov-Sachs (K–S) orientation relationship. The designed eutectic and near-eutectic HEAs exhibit a superior combination of high strength and ductility within a certain compositional range, outperforming most of other reported EHEAs. Specifically, the Ni49Fe28Al17V6 EHEA exhibit both high strength and large ductility, i.e., a yield stress of 760 MPa, a tensile stress of 1290 MPa and a fracture strain of 26.5 %, respectively. Furthermore, the high strength of the designed EHEA originates not only form the interface strengthening of FCC/L12 and B2 phases, but also from the inhibition of dislocation slipping by the ordered L12 nanoprecipitates. The stable K–S interface endows the designed EHEA with exceptional strength-ductility combination. The alloy-design strategy in this work provides new insights for the exploration of high-performance structural alloys in the future.