In this paper, we present the dynamic modeling and model predictive tracking control for a fin-actuated robot with barycentre regulating mechanism in multiple motions. Specifically, a dynamic model for the robot is established firstly. Based on the dynamic model, a model predictive tracking control algorithm is proposed. And simulations of of tracking rectangle trajectory, sine-like trajectory, ascending trajectory, and spiral trajectory are conducted to validate the algorithm. The simulation results demonstrate that the proposed algorithm is able to implement trajectory tracking of the robot with small position error and orientation error. This paper contributes to trajectory tracking for an underwater robot with controllable barycentre in multiple motions, which has been rarely explored.