The study to give electrical conductivity by dispersing carbon nanotubes (CNT) into silicon nitride ($Si_3N_4$) ceramics has been carried out in recent years. However, the density and the strength of $Si_3N_4$ ceramics were degraded and CNTs disappeared after firing at high temperatures because CNTs prevent $Si_3N_4$ from densification and there is a possibility that CNTs react with $Si_3N_4$ or $SiO_2$. In order to suppress the reaction and the disappearance of CNTs, lower temperature densification is needed. In this study, $HfO_2$ and $TiO_2$ was added to $Si_3N_4-Y_2O_3-Al_2O_3$-AlN system to fabricate CNT-dispersed $Si_3N_4$ ceramics at lower temperatures. $HfO_2$ promotes the densification of $Si_3N_4$ and prevents CNT from disappearance. As a result, the sample by adding $HfO_2$ and $TiO_2$ fired at lower temperatures showed higher electrical conductivity and higher bending strength. It was also shown that the mechanical and electrical properties depended on the quantity of the added CNTs.