We report the temperature dependent current (I) – voltage (V) characteristics of Fe3O4 nanowires with varying width (w) of 132, 358, and 709nm. While the widest nanowire (w=709nm) shows ohmic I (V) curves for all temperatures, those for w=132 and 358nm show nonlinearity, which can be expressed by a combination of linear (V) and cubic (V3) terms. The behaviour of conductance (linear bias component of current) and non-linearity in these nanowires is related to small polaron hopping related conduction. Moreover, we observed an anomalously large hopping lengths, which may be related to the size of percolation cluster and/or antiphase domain. Our study presents first experimental evidence for such non-linear polaronic conduction in magnetite nanowires.