Uranium present in low concentration in ocean water has the potential to greatly augment the current fuel reserve for nuclear power generation, but the challenge of extracting it economically remains. Two new designs of seawater uranium extraction systems are proposed in this paper—a stationary system and a continuous system—both of which utilize a braided polymer adsorbent. The stationary system simplifies the recovery procedure, and it is predicted to produce uranium at $326/kg. The continuous system is attached to an offshore wind turbine system to eliminate the need for additional mooring and increase the overall energy-gathering ability of the wind farm system. This system could maximize the adsorbent yield and achieve a production cost of $403/kg of uranium.