In this work, we investigated the effect of Cu doping on the energetic, structural, and electronic properties of (Zn1-x Cu (x) )(5)(OH)(6)(CO3)(2) (0 a parts per thousand currency sign x a parts per thousand currency sign 0.5) by density functional theory (DFT). Our calculation results demonstrate that (Zn0.6Cu0.4)(5)(OH)(6)(CO3)(2) is the most stable structure in thermodynamics. Cu atoms prefer to occupy Zn-1 + Zn-2 + 2Zn(3) sites in the case of x = 0.4. The calculated equilibrium lattice constants and average bond lengths agree well with the available experimental results. With increasing the amounts of Cu dopant (0.1 a parts per thousand currency sign x a parts per thousand currency sign 0.4), the covalent features of Cu-doped Zn-5(OH)(6)(CO3)(2) systems are gradually weakened, while the Cu-2 site exhibits the strongest Jahn-Teller distortion. Besides, the calculated population analysis illuminates the variation of -OH infrared stretching vibration frequency and the thermal decomposition order of CO3 (2-). The TDOS curve of (Zn0.6Cu0.4)(5)(OH)(6)(CO3)(2) shifts to the lower energy region than other systems, confirming its thermodynamic stability. Moreover, hydrogen locations are determined by performing structural optimization using DFT. These derived computational findings of (Zn1-x Cu (x) )(5)(OH)(6)(CO3)(2) are expected to help improve our fundamental understanding of improving the Cu/ZnO catalysts.