Since flow instability may deteriorate thermal hydraulic conditions, the natural circulation flow stability analysis of a small reactor has been researched in the present study by using the RELAP5 code. The influence of core power and moderator reactivity feedback under steady-state conditions and transient operation conditions is carried out. The results show that the core power and moderator reactivity feedback have an effect on the natural circulation flow stability of the primary loop of the small reactor. The small reactor has high stability when operated at high power, while the oscillation of the system at low power is slightly increased, and the stability time is delayed. Moderator reactivity feedback has influence on the stabilization process of the system. Under the reactivity feedback of the moderator with a larger absolute value, the flow transient response appears overshoot. Based on the calculation results, a hypothetical condition is simulated, and the calculation results prove that the reactor trip signal of the core outlet (ascending section) low subcooling can protect the small reactor within the design range from appearing natural circulation flow instability. Furthermore, the reactor core main flow region is changed from a single channel model to a closed parallel multi-channel model. The assembly power factor limit in closed parallel multi-channel is studied. It is recommended that the power factor of each assembly should be restrained in the fuel management design to avoid flow instability.