We report the influence of the field effect on the dc resistance and Hall coefficient in the strain-induced Mott insulating state of an organic superconductor kappa-(BEDT-TTF)(2)Cu[N(CN)(2)]Br. Conductivity obeys the formula for an activated transport sigma(square)=sigma(0)exp(-W/k(B)T), where sigma(0) is a constant and W depends on the gate voltage. The gate-voltage dependence of the Hall coefficient shows that, unlike in conventional field-effect transistors, the effective mobility of dense hole carriers ( approximately 1.6x10(14) cm(-2)) is enhanced by a positive gate voltage. This implies that carrier doping involves delocalization of intrinsic carriers that were initially localized due to electron correlation.