To investigate leakage current density versus electric field characteristics, epitaxial EuTiO3 thin films were deposited on (001) SrTiO3 substrates by pulsed laser deposition and were post-annealed in a reducing atmosphere. This investigation found that conduction mechanisms are strongly related to temperature and voltage polarity. It was determined that from 50 to 150 K the dominant conduction mechanism was a space-charge-limited current under both negative and positive biases. From 200 to 300 K, the conduction mechanism shows Schottky emission and Fowler-Nordheim tunneling behaviors for the negative and positive biases, respectively. This work demonstrates that Eu3+ is one source of leakage current in EuTiO3 thin films.