Since their discovery, electrically conductive polymers have attracted attention due to their properties such as corrosion resistance, electrical conductivity, and low density. The property of electrical conductivity is made possible by the alternating arrangement of single and double bonds and the introduction of a free charge carrier. One of the main representatives of electrically conductive polymers is poly(3,4-ethylenedioxythiophene) (PEDOT) due to its good chemical stability, biocompatibility, low production cost and electrical conductivity in the semiconductor field. The introduction of poly(ethylene glycol) side branches (PEG) improves stretchability and flexibility due to the formation of non-covalent cross-links by hydrogen bonding, allowing potential application in the field of portable electronics. With additional crosslinking agents, it is possible to achieve full covalent crosslinking, which further increases the extensibility and also improves the resistance to chemicals. The synthesis of the graft copolymer was carried out in four steps. In the first step, the bromofunctionalized thiophene monomer ThBr was synthesized, and in the second step, the macroinitiator PEDOT-Br was synthesized. The graft copolymer PEDOT-g- PEG was then synthesized by grafting PEG side chains onto the PEDOT-Br main chain by atom transfer radical polymerization (ATRP). In the fourth step, ATRP was performed again with an additional crosslinking agent (2-oxo-1,3-dioxolan-4-yl)methyl methacrylate (GCMA) to obtain the covalently crosslinked conducting polymer X-PEDOT-g- PEG. The obtained samples were characterized by nuclear magnetic resonance (NMR), Fourier transform infrared spectroscopy (FTIR), thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC). The obtained samples were used to prepare inks for inkjet printing on a flexible polyurethane substrate (PU). The printed layers on the substrate were tested for electrical conductivity and mechanical deformability. The results of FTIR and NMR analysis confirm the success of PEDOT-g- PEG synthesis, while DSC analysis shows that the glass transition temperature is below the body temperature (37 °C), which allows the sustainability of the graft copolymer in contact with the skin. The electrical conductivity values are in the range of semiconductors, and a strain of 50% does not cause permanent deformation, while no significant change in electrochemical activity was observed. Based on the overall results, the synthesized graft copolymer PEDOT-g- PEG could have a potential application in the field of wearable electronics.