For a composite of poly(lactic acid) containing graphene nanoplatelets (GNPs) at a low concentration (0.34 vol%), this study examined growths of mechanical and electrical properties under an alternating current (AC) electric field, focusing on field-induced GNP structures governing those properties. The composite was subjected to the AC field (60 Hz) of various intensities E for various times t (E) at 190 A degrees C. A fraction of randomly oriented GNPs was aligned by the field and then connected into columns, as suggested from optical microscopy. This structural evolution led to qualitatively similar growths of low-frequency storage modulus and static electrical conductivity. The key quantity for understanding this growth was a time t (E)* for occurrence of short circuit that detected formation of GNP columns conductively bridging the electrodes. The growths of both modulus and conductivity for various E were summarized as functions of a reduced variable, t (E)/t (E)*, confirming the growths commonly reflected the evolution of the GNP columns. However, the modulus grew fast and leveled off by t (E)/t (E)* similar to 1, whereas the conductivity kept growing gradually even at t (E)/t (E)* > 1. This difference was discussed in relation to the matrix chains and leftover GNPs out the column.