Tracked vehicles are widely used as seabed production tools to ensure a stable motion on soft sediments. However, the slippage resulted from the complex nonlinear trackterrain interaction while trajectory tracking causes problems for precisely predicting the motion. Accordingly, a "proper" motion control method is necessitated. This work proposes a novel dynamic modeling approach and motion control method for seabed tracked vehicles under nonholonomic constraints, with the inclusion of the effects of the bulldozing resistance, compaction resistance, water resistance, and the direction and velocity of the current. The back-stepping control based on a model-based proportional-integral-derivative three degrees-of-freedom method is applied in the controller, and its stability is proven by Lyapunov theory. The effectiveness and accuracy of the method in controlling seabed tracked vehicles are validated by simulation examples.