The availability of a reliable and sufficient amount of water constitutes one of the Sustainable Development Goals set by the United Nations. The provision of water is still challenging in many regions of the world, especially in arid and semi-arid regions, where the precipitations are rare and there is no access to water bodies. We propose to use a water harvesting device based on high-performance membranes to produce water from air in a decentralized way. The device presents a single membrane stage to increase the purity of water vapor in air and a condenser to produce liquid water. We optimize the operating conditions to bring down the water cost to 3.2 cent/L when the water fraction in air is 3% and 5.0 cent/L when the water fraction is 2%. We also found that the increase of water vapor permeance up to 5 x 104 gas pemeation units is beneficial to cost reduction (between 2.2 and 3.0 cent/L) and that the losses due to concentration polarization can be reduced by designing properly the channel geometry. Finally, we simulated the yearly operation of a device located in a semi-arid region, by taking into account the variation of water vapor concentration in air, and we found attractive values of water cost, below 10 cent/L for most of the year. Thus, the proposed process can give an important contribution to the alleviation of water shortage issue in semi-arid regions. Importantly, it makes membrane-based process attractive for atmospheric water harvesting.