The floating storage and regasification unit (FSRU) has several large LNG tanks in the body. Under unloading conditions, the mass of liquid in the cabin changes dynamically, and the time-varying mass of liquid can have a transient sloshing phenomenon when excited by waves. In this paper, a physical model experiment was carried out to study the transient sloshing characteristics of time-varying mass liquid in a rectangular tank, and the influence of the mass change rate of liquid and the initial water depth in the tank on the sloshing time-history characteristics of liquid under different excitation conditions was analyzed. It is found that the sloshing of time-varying mass liquid has significant nonlinear characteristics. Under the same excitation conditions, the maximum relative slosh amplitude of the liquid in the tank increases with the increase of the initial water depth, but decreases with the increase of the liquid mass change rate and the excitation amplitude.