In this paper, the trajectory control problem of an underwater robot is addressed. From the viewpoint of control engineering, trajectory control of the underwater robot is not an easy task due to its nonlinear dynamics, which includes various hydraulic forces such as buoyancy forces and hydrodynamic damping, the difference between the centers of buoyancy and gravity, and disturbances from a tether cable. To solve such problems, we applied Time Delay Control to the underwater robot. This control law has a very simple structure not requiring the nonlinear plant dynamics, and was proven to be highly robust against disturbances and uncertainties. We confirmed its effectiveness through experiments.