Abstract: The coolant flow in the core of the supercritical water reactor experiences drastic change (e.g. density) near the pseudo-critical point, which may be susceptible to density wave oscillation instability, so the stability is a great challenge to the supercritical water reactor. In the paper, the method of frequency domain analysis was used to study the stability of the fast spectrum zone. The stability boundary was given, and sensitivities of some parameters such as mass flow, system pressure drop, axial power distribution and hot channel division were generated. The result shows that a high mass flow and a high system pressure drop are beneficial to the system stability. The higher power density of a hot channel is, the worse stability of the system is. These results can provide a little guidance to the supercritical water reactor core design and optimization.