In this study, a data-driven hydrodynamic modeling method for a flippers-driven underwater vehicle-manipulator system (F-UVMS) is proposed. The modeling method combines parameter identification technique and computational fluid dynamics simulation, which makes the acquisition of hydrodynamic coefficients efficient and convenient. The hydrodynamic analysis of the biomimetic flipper propulsor is completed and the relationships between the generated forces and the motion parameters of the biomimetic flipper propulsor are revealed. The wake effects are analyzed to reveal the mechanism of the biomimetic flipper propulsor. Lift and drag coefficients are identified by the hydrodynamic data and the dynamic model of the biomimetic flipper propulsor is derived. The proposed hydrodynamic model is applied to the position control strategy of the F-UVMS. The motion experiments of the F-UVMS are conducted in the sea and the motion patterns of the F-UVMS are validated.