The invention relates to a recombinant cell, preferably a yeast cell comprising: a) one or more heterologous genes encoding a glycerol dehydrogenase activity; b) one or more genes encoding a dihydroxyacetone kinase (E.C. 2.7.1.28 and/or E.C. 2.7.1.29); c) one or more heterologous genes encoding a ribulose-1,5-biphosphate carboxylase oxygenase (EC 4.1.1.39, RuBisCO); and d) one or more heterologous genes encoding a phosphoribulokinase (EC 2.7.1.19, PRK); and optionally e) one or more heterologous genes encoding for a glycerol transporter. This cell can be used for the production of ethanol and advantageously produces little or no glycerol.