In recent years, Remotely Operated Vehicles (ROVs) have played an increasingly important role in the construction and monitoring of underwater pile foundations. However, due to the open frame structure of such vehicles, a gap of knowledge still exists with regard to their hydrodynamic behavior. In this study, the hydrodynamic stability of such vehicles is investigated numerically by means of a multiple reference frame method. The hydrodynamic characteristics of the ROV when it moves horizontally and upward in the vertical plane are examined. It is found that there is interference between the horizontal and vertical thrusters of the ROV. There is also interference between the propeller thrust and drag (or lift). The effect of the vertical thrusters can increase the horizontal thrust by about 5%. The horizontal thrusters create a low-pressure area below the body, which can make vertical drag experienced by the ROV significantly higher.