Hypersonic vehicles are subjected to random vibration loads during flight, causing fuel sloshing in the tank, which leads to fatigue failure of the tank weld and affects flight safety. The additional mass method was used to equivalently replace the complex fluid-structure coupling calculation under random vibration loads, and the weld stress was obtained. Then, the three-interval method and the nominal stress method were applied to analyze the fatigue life of the fuel tank weld, and fatigue experiments on the tank weld were carried out for verification. The results show that under the equivalent random loads, the liquid level in the tank does not slosh significantly, indicating that the additional mass method is feasible. The maximum equivalent stress of the weld increases with increasing tank load, and the equivalent stress under the y-direction load is the largest. The predicted fatigue lives at full load and half load are 0.27 h and 0.10 h, respectively, while the experimental lives are 0.48 h and 0.17 h. The predicted lives are close to the experimental lives, which verifies the rationality of the method used in this study and provides a theoretical basis for the fatigue life prediction of fuel tank welds under sloshing and vibration.