Abstract: For natural circulation, it is shown that the flow in inverted U-tubes is unsteady, and the water in some inverted U-tubes flows backward. Based on the assumption of Boussinesq, one-dimensional governing equations about the water level of steam generator secondary side were established. The effects of water level of steam generator secondary side on the flow instability were analyzed by using the linear perturbation theory, and the RELAP5/MOD3.2 code was used to simulate the phenomena. The results show that as the inlet condition of inverted U-tube is unchanged, the characteristic pressure drop of flow in inverted U-tube increases and the characteristic mass flow rate decreases with the decrease of water level of steam generator secondary side, meanwhile, the stability parameters of inverted U-tube increase, so the water flows backward in inverted U-tube which will occur more easily with the decrease of water level of steam generator secondary side, and it is easier for the longer U-tube to flow backward.