Results of a 2-D transport model for a gas diffusion electrode performing CO2 reduction to CO with a flowing catholyte are presented, including the concentration gradients along the flow cell, spatial distribution of the current density and local pH in the catalyst layer. The model predicts that both the concentration of CO2 and the buffer electrolyte gradually diminish along the channels for a parallel flow of gas and electrolyte as a result of electrochemical conversion and nonelectrochemical consumption. At high single-pass conversions, significant concentration gradients exist along the flow channels leading to large local variations in the current density (>150 mA/cm2), which becomes prominent when compared to ohmic losses. In addition, concentration overpotentials change dramatically with CO2 flow rate, which results in significant differences in outlet concentrations at high conversions. The outlet concentration of CO attains a maximum of 80% along with 5% CO2 and 15% H2, although the maximum single-pass conversion is limited to below 60% due to homogeneous consumption by the electrolyte. Fundamental and practical implications of our findings on electrochemical CO2 reduction are discussed with a focus on the trade-off between high current density operation and high single-pass conversion efficiency.