Based on surveying the existing binary phase diagrams with eutectic points, a strategy of designing eutectic high entropy alloys (EHEAs) with desired high strength and ductility is proposed. Based on the computer-aided thermodynamic calculations, the pseudo eutectic binary alloy system of CoCrFeNiNbx (x = 0.1, 0.25, 0.5 and 0.8) was designed. The experimental results show that the eutectic alloys are composed of a ductile face centered cubic (FCC) phase and a hard Laves phase with fine laminar structures. The designed alloys show excellent integrated mechanical properties of ductility and strength. For the CoCrFeNiNb0.5 alloy, the compressive fracture strength and strain can reach above 2300 MPa and 23.6%, respectively.