Strengthening the CoCrFeNi high entropy alloy with a face-center cubic structure has become a research prospect in the last decade. Alloying with double elements, Nb and Mo, is an effective method. In this paper, to further enhance the strength of the Nb and Mo contained high entropy alloy, CoCrFeNiNb0.2Mo0.2was annealing treated at different temperatures for 24 h. As a result, a new kind of Cr2Nb type nano-scale precipitate with a hexagonal close-packed structure was formed, which is semi-coherent with the matrix. Moreover, by adjusting the annealing temperature, the precipitate was tailored with a considerable quantity and fine size. The best overall mechanical properties were achieved in the alloy annealed at 700 °C. The yield strength, ultimate tensile strength, and elongation are 727 MPa, 1.05 GPa, and 8.38%, respectively. The fracture mode of the annealed alloy is a mixture of cleavage and necking-featured ductile fracture. The approach employed in this study offers a theoretical foundation for enhancing the mechanical properties of face-centered cubic high entropy alloys via annealing treatment.