CO2 capture and storage (CCS) is considered as a key strategy in the short to medium term to mitigate global warming. The Calcium-Looping process, based on the reversible carbonation/calcination of CaO particles, is a promising technology for post-combustion CO2 capture because of the low cost and non-toxicity of natural CaO precursors and the minor energy penalty on the power plant in comparison with amines capture based technologies (4-9 % compared to 8-12 %). Another interesting process to reduce CO2 emissions in power plants is oxy-combustion, which is based on replacing the air used for combustion by a highly concentrated (~95 % v/v) O2 stream. This work proposes a novel process (mOxy-CaL) for post-combustion CO2 capture based on the integration of membrane separation, partial oxy-combustion and the Calcium-Looping process. An oxygen-enriched air stream, which is obtained from air separation by using highly permeable polymeric membranes, is used to carry out partial oxy-combustion. The flue gas exiting partial oxy-combustion shows a CO2 concentration of ~30 % v/v (higher than 15 % v/v typical in coal power plants). After that, the flue gas is passed to the CaL process where the CO2 reacts with CaO solids according to the carbonation reaction. Thermogravimetric analysis show that the multicycle CaO conversion is enhanced as the CO2 concentration in the flue gas stream is increased. Process simulations show that the mOxy-CaL process has a high CO2 capture efficiency (~95%) with lower energy consumption per kg of CO2 avoided than previously proposed post-combustion CO2 capture technologies. Moreover, the overall system size is significantly lower that state-of-the-art CaL systems, which allows for an important reduction in the capital cost of the technology.