By employing density functional theory calculations, the mechanical, electronic and piezoelectric properties of graphene-like monolayers ZnO (g-ZnO) and GaN (g-GaN) were investigated. Elastic stiffness constants and piezoelectric tensors of monolayers g-ZnO and g-GaN using their Clamped-ion and Relaxed-ion components were mainly studied. Results indicate that these two graphene-like structures are semiconductors with excellent elasticity. The piezoelectric coefficient of monolayers g-ZnO and g-GaN are about 9.4 and 2.2 pm·V^-1, respectively, implying their piezoelectric effect in extremely thin film devices, especially the g-ZnO. The remarkable piezoelectricity of monolayer g-ZnO enables it a wide range of applications, such as mechanical stress sensors, actuators, transducer and energy harvesting devices.