A concept for a continuous supercritical drying process for the efficient production of aerogel particles is presented and proven experimentally. A process design involving a countercurrent extraction column with freely sedimenting aerogel particles is proposed and the influence of operating parameters such as temperature, pressure, and CO2 load on the process is discussed from a theoretical point of view. A proof of concept of the most promising design is demonstrated through the successful countercurrent drying of alginate aerogel particles. At a column length of 1.0 m, dry aerogel particles could be obtained at the bottom of the column with ethanol outlet mass fractions up to 46% at the top of the column. Drying of aerogel particles at a shorter column length of 0.5 m could be achieved by increasing the CO2 flow rate, resulting in a reduced ethanol outlet mass fraction of 20%. Further development of the continuous drying concept is discussed.