Carbon spheres from natural biopolymers (alginate and chitosan) are easily synthesised by thermal treatment between 400 and 800 °C under an inert atmosphere. All the samples, including the untreated natural biopolymers, as well as the resulting carbon materials, exhibit a remarkable CO2-adsorption capacity. The sample that exhibits the highest adsorption capacity was that obtained by carbonisation of alginate at 800 °C and subsequent treatment with KOH at 800 °C. This material exhibits a specific surface area of 765 m2 g−1, specific micropore volume of 0.367 cm3 g−1, ultra-micropore volume of 0.185 cm3 g−1, average ultra-micropore size of 0.7 nm and CO2-adsorption capacity of 5 mmol g−1 measured at 0 °C and atmospheric pressure. This value is close to the absolute record for CO2 adsorption and, by far, the highest if we compare unit areas or consider the density of the material. The combination of the high N content already included in the chitosan structure and the elevated microporosity in the case of alginate are crucial factors to obtain these satisfactory values with an easy and green preparation procedure. Also, owing to the high conductivity of the alginate-derived carbon (better than graphite), it has been possible to develop a process of reversible adsorption–desorption by applying a voltage, which is a low-energy desorption method compared with the conventional method of vacuum and high temperatures. All these properties, together with the spherical shape of the material of 0.1 mm, which is the most suitable form to favour mass transfer in fluidised-bed reactors, make this material a highly promising adsorbent for industrial applications.