Varying quantities of a high-thermal-expansion glass, 50CaO-20ZnO-$20B_2O_3-10SiO_2$ (CZBS), were added to alumina and sintered at $875^{circ}C$ for 2 h for low temperature co-firing ceramic (LTCC) applications. As the amount of glass addition increased from 40 wt% to 70 wt%, the apparent density of the sintered product increased from 88.8% to 91.5%, which was also qualitatively confirmed by microstructural observation. When the glass addition was very high, e.g., 70 wt%, an apparent formation of secondary phases such as $CaZn_2AlZnSiAlO_7$, $Ca_2Al(AlSi)O_7$, $Ca_2Al_2SiO_7$, $Ca_2ZnSi_2O_7$ and ZnO, was observed. Both the dielectric constant and the coefficient of thermal expansion increased with the glass addition, which was qualitatively consistent with the analytical models, while the experimental values were lower than the predicted ones due to the presence of pores and secondary phases.