This for a spacecraft undergoing a continuous thruster maneuver, the spacecraft mass changes due to fuel consumption, and the liquid sloshing has time-varying property. However, the conventional applications in prior literature took these time-varying properties into consideration barely. The characteristics of residual fuel become an important drive for the coupled solid-liquid dynamics, especially in a partially filled tank. In this paper, dynamic equations of an equivalent pendulum model with variable parameters were developed by Lagrangian method. The calculation results showed that the time-varying properties influence the sloshing characteristics significantly. Finally, influences of draining flow rates, the thrust press during the sloshing motions, sloshing induced forces and torques were also investigated. The investigations here provided an effective way to deal with the delicate problem and to reveal the characteristics of the liquid sloshing dynamics in partially filled tank of a spacecraft.