Linear poly(ether-urea-imide)s (PUIs) are attractive multi-block segmented copolymers well-known for high selectivity for CO2 separations. Their CO2 permeability generally increases but their selectivity decreases with their polyether soft content limited to 70 wt% to preserve their mechanical properties. In this work, the grafting of a PUI copolymer with PEO-based soft grafts is reported for strongly increasing the membrane properties. The design of the grafted copolymers involved step-growth polymerization, controlled radical polymerization, and "click" chemistry. This strategy ensured the control of grafting rate, graft molecular weight and soft contents varying from 57 to 85 wt%. The membrane properties for CO2 and N2 permeation were correlated to the PUI chemical structure, morphology and soft content. The best membrane properties (PCO2 = 196 Barrer; alphaCO2/N2 = 39 at 2 bar and 35°C) were obtained for PUI-g-1PEDEGA5000 corresponding to the highest grafting rate and graft length. Compared to the non-grafted PUI, the best grafted copolymer had much higher CO2 permeability (×17) while the ideal separation factor alphaCO2/N2 was maintained at high level, thus leading to separation properties very close to the Robeson 2008 upper-bound. By allowing very high contents of amorphous soft phase and specific morphology, the new grafting strategy offered high-performance membranes for CO2 capture.