The electrical conductivity of a iodine-doped polyacetylene is measured as a function of the electric field Escr at temperatures between 4K and 0.3K. We find that after an initial non-linear behavior sgr increases linearly with Escr in agreement with a theoretical description based on variable-range hopping conduction. The non-linear rise at low fields depends on the iodine concentration. In heavily doped samples the increase is small and varies as Escr2, whereas in less conductive samples a large change is observed at 0.3K which varies approximately as log Escr for fields from 1 V/m to 150 V/m.