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The Cu–Cr–Zr–Nb alloy bars were prepared by vacuum melting, hot forging, solution treatment, and drawing. The effects of aging processes on the microstructure, texture, mechanical properties and electrical conductivity of the alloy were studied, and the precipitation kinetics was analyzed. Besides, the effect of adding Nb to the Cu–Cr–Zr alloy was simulated by the first-principles calculation. The results showed that when the aging temperature increased from 400 °C to 460 °C, Cube texture and Brass texture were transformed into Copper texture. The Cu–Cr–Zr–Nb alloy exhibited superior comprehensive properties such as a hardness of 84.3 HRB, a tensile strength of 520 MPa, an elongation of 19.0 %, and an electrical conductivity of 83.5 International Annealed Copper Standard (%IACS) after being aged at 460 °C for 4 h. The precipitation kinetics and electrical conductivity equations under different aging temperatures were established, and the precipitation activation energy of 24 kJ/mol was obtained. Moreover, the precipitation process of the alloy was also described by the Avrami empirical equation. It was found that the reaction mechanism of the alloy changed from nucleation and growth to one-dimensional diffusion as the aging temperature increased from 400 °C to 520 °C. It was also confirmed that Nb and Cr formed the Cr2Nb compound according to the first-principles calculation.