A three-dimensional mathematical ecosystem model has been combined with a circulation and a sea-ice models of the Barents Sea. The ecosystem model describes the interaction of phytoplankton, zooplankton, dissolved inorganic nitrogen, total inorganic carbon, alkalinity, organic and inorganic parts of detritus. The paper presents the results of calculations of the chlorophyll-a concentration in the period of maximum spring phytoplankton bloom in the Barents Sea, as well as the results of calculations of CO2 flux between the atmosphere and the sea under various conditions. The correspondence between the zones of the intensive growth of phytoplankton during the bloom period and the position of the Polar Front has been demonstrated. The estimation of the ocean-atmosphere CO2 exchange intensity in the presence and absence of the biological CO2 pump has been carried out. For the case without taking into account the oceanic biological uptake of atmospheric carbon dioxide it was found that the maximum values of CO2 flux can be observed in the areas of the ice edge. Taking into account the oceanic biological uptake of atmospheric CO2 leads to the spatial correspondence of the zones of maximal CO2 flux from the atmosphere and the zones of high primary production in the ocean surface layer. The results of the present study show that the spatial variability of the carbon dioxide flux from the atmosphere to the ocean is determined by the spatial variability of the primary production to a much greater extent than by the variations in the sea surface temperature.