In this study, we prepared a range of high-entropy alloys (HEAs), denoted as CoCrFeNiZrxNb(0.4−x) (x = 0, 0.1, 0.2, 0.3, 0.4), through vacuum arc melting. The synergistic impact of Zr and Nb alloying on the microstructure, mechanical properties and corrosion resistance of these HEAs was investigated. Each alloy comprises a face-centered cubic (FCC) phase and the Zr(Nb)-rich Laves phase. Additionally, a novel Ni7Zr2 phase precipitates in the CoCrFeNiZr0.2Nb0.2 HEAs. The two distinct intermetallic phases and the FCC matrix intertwine, creating a typical hypoeutectic structure. Furthermore, the synergistic impact of solid solution strengthening, precipitation strengthening, and fine grain strengthening in CoCrFeNiZr0.2Nb0.2 HEAs results in high values of yield strength and ultimate strength of 810 MPa and 1595 MPa, respectively, while maintaining a commendable compressive strain of 21.15%. Moreover, the corrosion resistance of the investigated HEAs initially rises and then declines with the continuous increase in Zr content. This trend is associated with the preferential onset of pitting corrosion in the Zr(Nb)-rich Laves phase region. Notably, the passivation film of CoCrFeNiZr0.2Nb0.2 HEAs proves to be the most stable among the five HEAs due to its fine grain size and the presence of beneficial oxides. Consequently, the corrosion resistance of CoCrFeNiZr0.2Nb0.2 surpasses that of the other HEAs under consideration.