Based on binary phase diagrams and thermodynamic calculation, CoCrFeNiTax (x = 0.1, 0.3, 0.43, 0.5 and 0.7) eutectic high entropy alloys were designed. With increasing Ta content, as-cast microstructure changed from hypoeutectic (primary γ phase) to eutectic and to hypereutectic (primary Laves phase), and CoCrFeNiTa0.43 eutectic alloy was composed of γ phase with face-center cubic (FCC) structure and C14 type Laves phase with hexagonal close-packed (HCP) structure. Volume fraction of Laves phase increased with increasing Ta content, and thus microhardness was basically positive correlation with Ta content. Meanwhile, microhardness and elastic modulus of primary phase increased from primary γ phase to primary Laves phase, while hardness and elastic modulus of eutectic phases firstly decreased and then increased with increasing Ta content. In addition, based on nanoindentation load-displacement curves, the reverse analysis algorithms were used to obtain initial yield stress σy and strain hardening exponent n of primary γ phase and eutectic phases. Moreover, with increasing Ta content, the plasticity of CoCrFeNiTax alloys decreased, while the compression strength firstly increased and then decreased, and CoCrFeNiTa0.43 EHEA showed relatively high strength (2377 MPa) and relatively high plastic strain (17.5%).