This paper proposes a hydrodynamic mathematical model of a tethered underwater robot system by introducing boundary conditions and coupling relations into the existed governing equations for umbilical cable systems. A feed-forward and feedback control method was used for adjusting the length of the umbilical cable while the incremental PID algorithm was applied on regulating rotating speeds of propellers for establishing the integral hydrodynamic and control model of a tethered underwater robot. The experimental validation and hydrodynamic responses under the two control manipulations were simulated numerically. The simulation results showed that the proposed model was valid and reliable. In the depth control, the maximum errors of pitch, roll and submerged depth of the underwater robot between simulation and experiment are 2°, 1° and -50 mm respectively. The errors of trajectory tracking simulations in X direction and Z direction are 10% and 15% respectively. The motion in Z direction of the underwater robot is determined mainly by the feed-forward and feedback control strategy for the cable, and the motion in X direction of the underwater robot is primarily controlled by the PID algorithm for regulating the rotational speeds of the duct propellers. The hydrodynamic loadings on the robot are influenced by the flow fields around the robot, and the changes of the flow fields are determined by the changes of the robot velocity and the propellers rotating speed.