A newly prepared organic conductor, (EDT-TSF)(2)GaCl(4), shows considerable nonlinear conductance in the insulating state below 20 K, and a metallic state is restored by the application of moderate currents. This conductor has a stacking structure with a quasi-one-dimensional open Fermi surface, similar to the sulfur analogues. Since the interchain interaction is enhanced by the selenium substitution, the static magnetic susceptibility as well as ESR does not show any anomaly around 20 K, and low-temperature X-ray investigation does not show any extra spots. Isostructural (EDT-TSF)(2)FeCl(4) shows similar conducting properties, although the magnetic interaction of the anion is weak. Like this, nonlinear conductance is a versatile tool to restore a metallic state when the metal-insulator transition is almost suppressed.