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Local electrical conduction behaviors of polycrystalline La-doped BiFeO3 thin films have been investigated by combining conductive atomic force microscopy and piezoelectric force microscopy. Nanoscale current measurements were performed as a function of bias voltage for different crystal grains. Completely distinct conducting processes and resistive switching effects were observed in the grain boundary and grain interior. We have revealed that local electric conduction in a grain is dominated by both the grain boundary and ferroelectric domain, and is closely related to the applied electric field and the as-grown state of the grain. At lower voltages the electrical conduction is dominated by the grain boundary and is associated with the redistribution of oxygen vacancies in the grain boundary under external electric fields. At higher voltages both the grain boundary and ferroelectric domain are responsible for the electrical conduction of grains, and the electrical conduction gradually extends from the grain boundary into the grain interior due to the extension of the ferroelectric domain towards the grain interior. We have also demonstrated that the conduction dominated by the grain boundary exhibits a much small switching voltage, while the conduction of the ferroelectric domain causes a much high switching voltage in the grain interior.