Direct numerical simulations of binary electrolyte in an electrode channel with turbulent mass transfer are performed under limiting current condition and galvanostatic current conditions. Behaviors of turbulent concentration diffusion from electrodes to adjacent electrolyte in a wide range of Schmidt numbers are examined and mechanism of turbulent mass transfer in electrolytic processes is analyzed. A physical model for turbulent electrodes channel flow is established with electrochemistry theories as well as fluid dynamics. Effect of Schmidt numbers on turbulent mass transport, mean and fluctuating concentrations, mass transfer coefficient, Sherwood numbers, and instantaneous structures of concentration fields are exhibited and analyzed. It shows that mass transfer at electrodes in turbulent electrolyte is sensitive to current conditions.