The composite of CVD-grown Gr is a promising method for improving the electrical properties of Cu-based microscale materials. Almost all of the previous works focused on the CVD-grown continuous Gr. However, after the combination with surface of Cu substrate, the continuous Gr is prone to fracture or peeling when it is bent under strain in practical applications with low bending stability, leading to a decrease in its conductivity. In this study, significantly enhanced electrical properties and bending stability are demonstrated by synthesizing CVD-grown Gr sheets layers on microscale-diameter Cu wires, including 10.9% higher electrical conductivity and 7.9% higher maximum current density compared to commercial pristine Cu wires. After the test of bending cycles, Gr sheets/Cu wires exhibit extraordinary bending stability, with less than 1.3% conductivity changes for wires. In contrast, the continuous Gr/Cu wires show poor bending stability with a nearly 10% reduction in conductivity. Hence, the Gr sheets/Cu wires have significant advantages in practical applications.