CoCrNi medium entropy alloy (MEA) has potential applications in cryogenic environment due to its strength and plasticity enhancement at low temperatures. However, the poor strength at the room temperature limits its widespread application. In this work, the alloying element, Tantalum (Ta), was chosen to strengthen CoCrNi MEA and CoCrNiTa x MEAs with different Ta content were designed and prepared. The effect of Ta content on the microstructure and mechanical properties of the corresponding alloys were investigated. It was found that Ta-enriched Laves phase was formed due to the addition of Ta element. The alloy's microstructure experienced from hypoeutectic to eutectic, and then to hypereutectic morphology evolution with increasing Ta addition. CoCrNiTa 0.4 alloy was a fully eutectic microstructure with fine lamellar colonies. Its yield strength reached about 2150 MPa, which was greatly improved compared with CoCrNi MEA. In order to understand the strengthen mechanism of CoCrNiTa x MEAs, strength contribution of the alloy's individual phase to the lamellar colonies was investigated by the high-throughput nanoindentation mapping technique. It is indicated that Laves phase had very high hardness increasing from ≈16.12 GPa to ≈18.14 GPa, almost 3 times than that of FCC phase (≈6.03 GPa). The strengthening of CoCrNiTa x MEAs should be attributed to the production of the hard Laves phase and lamellar colonies.