The metal nuclear reactor vessel is wrapped with a steam coil structure, which can maintain the metal coolant as liquid and play a role in heat preservation. In the process, the steam flow in the tube will cause the vibration of the coil. If the coil deforms greatly during the vibration process, it may cause the damage and affect the service life of the coil. In order to study the flow-induced vibration (FIV) in the steam coil, this paper uses FLUENT software, applying large eddy simulation (LES) method, combining single-phase equivalence and segmented calculation methods to simulate the coil flow field. The fluid excitation force in different sections of the coil was obtained, and the time domain data was converted into frequency domain data. Then, random vibration response of the coil was analyzed based on power spectral density (PSD) in ANSYS Mechanical. Finally, fatigue analysis was carried out and fatigue life was predicted. The results show that the fluid excitation force in the coil decreases along the way, and the fluid excitation force at the elbows is obviously greater than that in the long tube bends. According to PSD solution, the maximum vibration displacement and velocity are very small, and the maximum stress occurs at the elbow position. Combined with fatigue analysis, the steam coil given in this paper meets the design requirements.