Electrical properties of AlN ceramics sintered with 1 wt% $Y_2O_3$ have been investigated. From the impedance spectroscopy, electrical conductivity of grain boundary was found to be much lower than that of grain. DC conductivity measurement showed the electrode polarization effects caused by blocking electrode. The heat-treatment at $1700^{circ}C$ of the specimen sintered at $1850^{circ}C$ transformed continuous pain boundary phases along triple boundary junctions into isolated particles in grain comers. The heat-treatment induced decreases both in grain and grain boundary conductivity, and in DC electrical conductivities. From the analysis on the transference number, ionic conductivity was shown to be more dominant than electron conductivity, which was due to ion compensation mechanism during oxygen incorporation into grain.