The development of 2D materials with excellent electronic properties and piezoelectric response is clearly critical for multifunctional piezoelectric devices. Herein, based on first-principles calculations, the electronic, mechanical, and piezoelectric properties of a series of 2D copper-based ternary chalcogenides, denoted as CuMX 2 (M ¼ Sb and Bi; X ¼ S and Se) monolayers, are systematically studied, which can be obtained by exfoliating from their bulk counterparts. The calculations show that these ternary CuMX 2 monolayers exhibit desirable dynamical and thermal stabilities and moderate bandgaps. The calculated piezoelectric coefficients d 11 and d 12 of these monolayers are in the range of 0.44-6.14 and 9.13-29.52 pm V À1 , respectively, which exceed or approach those of most well-studied 2D systems. Interestingly, as compared with other reported 2D systems, the CuMX 2 monolayers exhibit an anomalous anisotropy of piezoelectric response, manifested as the larger coefficient d 12 than coefficient d 11 .The study demonstrates that the CuMX 2 monolayers are potential 2D candidates in nanoelectric and nanopiezoelectric devices.