Si3N4 ceramic materials have great potential in the field of insulation in SF6 gas ultra-high-voltage transmission and transformation equipment due to their excellent insulation performance and thermal stability. In this paper, Y2O3-Al2O3 was used as a sintering aid to prepare high-density (>99%) Si3N4 ceramics through two-step pressureless liquid-phase sintering, and the mechanism of the influence of Y2O3-Al2O3 addition on the microstructure and electrical properties of Si3N4 ceramics was studied. The results showed that increasing the sintering aid content could increase the grain size of Si3N4 ceramics, while increasing the Y2O3 ratio could refine the grain size. When Y2O3-Al2O3 addition was 8% and the ratio was 5:3, the room temperature volume resistivity of Si3N4 ceramics was the highest, 7.33 × 1014 Ω·m, and the volume resistivity was the most stable when the sintering aid content was 12%. The internal carrier migration type of Si3N4 ceramics was mainly ion conduction, mainly along the grain boundaries. The temperature stability of the resistivity of Si3N4 ceramics could be improved by doping with Y3+ functional ions to reduce the potential barrier conductivity level and refine the grain size to improve the conduction path. The dielectric constant and dielectric loss of Si3N4 ceramics were mainly affected by interface polarization. They gradually increased with the increase in sintering aid addition. Temperature had little effect on dielectric constant and dielectric loss in the range of 20–80 °C.