Strong nonlinearity and the relevance of time-varying dynamic parameters in the maneuverable process of water-jet propulsion were major problems encountered in the prediction of variable acceleration dynamics characteristics. The relationships between the thrust and rotation speed of a screw mixed-flow pump, drag and submerged speed of water-jet propulsion were obtained from flume experiments and numerical calculations, based on which a dynamic model of pump-jet propulsion was established in this paper. As an initial condition, the numerical solution of the submerged speed with respect to time was inputted to computational fluid dynamics (CFD) for unsteady calculation based on a user-defined function (UDF). Thus, the relationships between the acceleration, drag, net thrust, propulsion torque and efficiency with respect to time were revealed. The results indicate that the relationship between the thrust and rotational speed of a water-jet propeller is a quadratic function, which agrees well with the experimental values. The variation of submerged speed with respect to time satisfies a hyperbolic tangent function distribution. The acceleration increases sharply at the beginning and then decreases gradually to zero, especially at high rotation speeds of the water-jet pump. The variations in drag and propulsion efficiency with respect to time coincide with the step response of a second-order system with critical damping. The method and results of this study can give a better understanding of the changes in dynamic parameters such as velocity, acceleration, thrust, and drag during the acceleration of a pump-jet submersible and helped to estimate the effects of pump performance on water-jet propulsion kinetic parameters.