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In order to analyze the spatial maneuverability of the remotely operated underwater vehicle (ROV), the 6-DOF motion mathematic model of the ROV was founded. Hydrodynamics were analyzed by using the Taylor series. The thrusters on the ROV were discussed. This paper considers three cases of motion simulation:vertical motion, rotational motion and Z-shape motion. A series of simulation experiments showed that the 6-DOF motion mathematic model was correct and reliable, and also fit with the scene simulation.