In fusion reactors, many blanket concepts are designed with water as a coolant to transfer high-density heat from the fusion reaction out of the reactor core. The coolant temperature and pressure are maintained as the validated use in water-cooled fission reactors. However, the flow channel in a water-cooled blanket is independent of each other, and there is no flow mixing between coolant channels. Therefore, flow instability may occur in the independent parallel channels in a water-cooled blanket due to its unique structure and heat distribution, especially under the high heat flux caused by plasma rupture. In this study, the parametric analysis of density wave instability is performed using a thermal-hydraulic code developed for independent parallel channels based on the homogeneous model for the two-phase flow. The parallel-channel system in a water-cooled ceramic breeder (WCCB) blanket of the China Fusion Engineering Experimental Reactor (CFETR) is established for its first wall structure. A small disturbance is introduced into the system to determine if it is stable under different conditions. It is found that the channel number has no obvious influence on the prediction of the flow instability boundary. Therefore, the two-channel system is adopted to investigate the influence of different parameters, such as the pressure, resistance, flow rate, and inclination, on the flow instability boundary of the parallel-channel system in the CFETR WCCB blanket. The results show that flow instability occurs more easily in this study compared to the traditional instability analysis, especially under high-pressure conditions. In general, conditions of high pressure, large flow rate, and no inclination can stabilize the system, while the influence of resistance is quite different under different conditions of resistance and pressure. The research work indicates that more attention should be paid to the joint influence of different parameters for the water-cooled blanket during its design and operation.