Silicon nitride ($Si_3N_4$) ceramics have been considered for various components of nuclear power plants such as the mechanical seal of a reactor coolant pump (RCP), the guide roller for a control rod drive mechanism (CRDM), and a seal support, etc. Corrosion behavior of $Si_3N_4$ ceramics in a high-temperature and high-pressure water must be elucidated before they can be considered as components for nuclear power plants. In this study, the corrosion behaviors of $Si_3N_4$ ceramics containing MgO and $Al_2O_3$ as sintering aids were investigated at a hydrothermal condition ($300^{circ}C$, 9.0 MPa) in pure water and 35 ppm LiOH solution. The corrosion reactions were controlled by a diffusion of the reactive species and/or products through the corroded layer. The grain-boundary phase was preferentially corroded in pure water whereas the $Si_3N_4$ grain seemed to be corroded at a similar rate to the grain-boundary phase in LiOH solution. Flexural strengths of the $Si_3N_4$ ceramics were significantly degraded due to the corrosion reaction. Results of this study imply that a variation of the sintering aids and/or a control (e.g., crystallization) of the grain-boundary phase are necessary to increase the corrosion resistance of $Si_3N_4$ ceramics in a high-temperature water.