Hypersonic vehicles are subjected to random vibration loads during flight, and the fuel in the tank shakes, leading to fatigue failure of the tank weld, which affects flight safety. In this study, the additional mass method is used to equate the complex fluid-structure coupling calculation of random vibration loads to obtain the tank weld stress; then, the life of the fuel tank weld was analyzed by applying the three-interval method and the nominal stress method, and the fatigue experiments of the tank weld were carried out for verification. The results show that: under the equivalent random load, the liquid level in the tank shaking is not obvious, and the additional mass method is feasible; the maximum equivalent force of the weld increases with the increase of the tank load, and the equivalent force under the y-direction load is the largest; the predicted lifetimes at full load and half load are 16 minutes and 6 minutes, and the experimental lifetimes are 29 minutes and 10 minutes; the predicted lifetimes are close to the actual lifetimes, which verifies the reasonableness of the method used in this paper. The predicted life is close to the actual life, which verifies the rationality of the method used in this paper, and provides a theoretical basis for the fatigue life prediction of fuel tank weld under sloshing and vibration.