Liebau pumping produces net directional flow via periodic compression of a compliant tube at an asymmetric location, eliminating the need for valves or check flaps. While attractive for its simplicity, this mechanism has rarely been explored for robotic propulsion. Here, we present the first free-swimming robot actuated solely by Liebau pumping. A soft silicone conduit is cyclically compressed off-center by a single solenoid actuator, generating traveling pressure waves that produce thrust. Directional control is achieved through simple frequency switching, enabling both forward and reverse swimming. Experimental results reveal distinct frequency bands that correspond to the forward and reverse swimming modes, with peak velocities of 5.25 cm/s forward at 11 Hz and –1.58 cm/s in reverse at 15 Hz using a 30% duty cycle and 1 A peak current. Agility tests confirm smooth, responsive transitions between directions without mechanical valves or moving parts. These results establish Liebau pumping as a viable, low-complexity propulsion method for soft and ecologically safe underwater robots.