Graphene-metal composites (GMC) possess superior properties, such as high specific strength, and high thermal and electrical conductivity, and have been widely used in many fields. However, the fabrication of GMC still remains to be explored, as existing methods via powder metallurgy and chemical synthesis are difficult to achieve uniform dispersion of graphene, not to mention achieving selective and localized preparation of GMC with complex patterns. In this paper, a simple method for the fabrication of graphene-copper composites (GCC) is firstly proposed by combining flexible laser irradiation and efficient electrodeposition. It not only effectively solves the problems of graphene agglomeration and inhomogeneous dispersion in GCC, but also enables the selective and precise preparation of GCC with spatial micro-patterns. Specifically, an ultrafast picosecond (ps) laser is firstly used to irradiate the polyimide (PI) film to selectively and precisely produce the desired laser-induced graphene (LIG) region. The localized deposition of copper atoms is subsequently made via the electrodeposition step, forming the flexible GCC with a laser-determined spatial pattern. The experimental study of LIG process on PI film has been carried out, and high-quality LIG region is obtained by optimizing the laser scanning path and parameters. On this basis, the regional flexible GCC of 45 μm in thickness with a compact and uniform copper layer of 20 μm has been efficiently fabricated, followed by the detailed characterizations of surface morphology and chemical composition. Furthermore, a significant enhancement of the electrical conductivity has been confirmed, as the measured value is up to 32.8 S/cm at the LIG region and further to about 60.9 S/cm at the GCC area. The mechanical properties of the obtained conductive GCC have been tested and good flexibility is confirmed by nanoindentation and bending tests, verifying its potential for a wide range of applications in flexible electronics, medical and many other fields.