Laboratory model tests were conducted in constant-voltage mode and constant-current mode for the one-dimensional electro-osmotic treatment of dredged sediment, with an approximately consistent initial electric power. The voltage, current, drainage rate, electro-osmotic transport volume, and energy consumption coefficient during the electro-osmotic process were measured and calculated. After treatment, the final soil moisture at designated positions in the test samples was measured to investigate the effects of different power supply modes. Further, the divergent phenomena observed with constant voltage and constant current were discussed. Based on an analysis of the measured energy consumption coefficients with time, we obtained a linear relationship between the applied/equivalent voltage and energy consumption coefficient. Furthermore, the electro-osmotic processes are divided into four stages by equal drainage quantity to obtain the energy consumption and electro-osmotic transport volume under different working conditions. The results reveal that the energy consumption of electro-osmosis is mainly determined by the applied voltage or the equivalent voltage for dredged sediment, while the value of electro-osmotic transport volume depends mainly on the change in soil water content rather than power supply modes. The drainage rate in constant-current mode was observed to be relatively steady, maintaining an approximately constant rate until the soil moisture was dramatically reduced. In other words, constant-current mode shows the advantages of being powerful and persistent in electro-osmotic treatment.