Dielectric breakdown constitutes an important limitation in the use of insulating materials under high-voltage since it can lead to the local fusion and sublimation of the insulator. The role of electrical charge transport and trapping in alumina ceramics on their resistance to this catastrophic phenomenon is studied in this work. In polycrystalline materials, the interfaces between the various phases play a main role because they constitute potential sites for the trapping of electrical charges. The density and the nature of these interfaces can be controlled by the way of the microstructure parameters. So, the aim of the present paper is to highlight the influence of average grain size and intergranular phase crystallization rate on the ability of polycrystalline alumina materials to resist to dielectric breakdown. Thus, it is shown that the control of the process conditions (sintering aids content, powder grain size and thermal cycle) makes it possible to change not only the density (by the average grain size) but also the nature (by the crystallization or not of anorthite) of the grain boundaries. On one hand, at room temperature a high density of interfaces, due to low grain size and highly crystallized intergranular phase, leads to a high dielectric strength. On the other hand, at higher temperature (250 degrees C), the presence of vitreous intergranular phase makes it possible to delay breakdown. That behaviour is explained thanks to charge transport and trapping characterizations.