Silver pastes as the outer electrodes have been prepared using Pb-free glass frits with different content of $Bi_2O_3$ and the effects of glass composition on the degradation behaviors of the Ag electrodes were investigated using the change of adhesion between Ag electrode and alumina substrate with thermal cycle stress. Low adhesion and high surface resistance were observed in Ag electrode using glass frit with a $Bi_2O_3$ content of 60 wt%, owing to the open microstructure formed at the firing temperature of $600^{circ}C$. When the $Bi_2O_3$ was increased to 80 wt% in the glass frit, the Ag electrodes had a dense microstructure with high adhesion and a low surface resistance. Delamination of the Ag electrodes was a major failure mode under thermal cycle stress and this was attributed to residual stress due to the thermal expansion mismatch between the Ag electrode and the alumina substrate.