The present manuscript is devoted to the study of the nonlinear optical absorption of a smectic liquid crystal doped with gold nanorods in the presence of an external electric field. By using Z-scan technique in the configuration of fully open aperture and normal incidence, we analyze the changes in the absorption coefficient of a homeotropic sample upon laser exposure. Our results reveal that the electric field may suppress the nonlinear absorption of the samples well bellow to smectic-A-nematic transition temperature. The effects of the external electric field on the interplay between smectic order and plasmon resonance are analyzed.