In this Paper, slack is computed from a comparision of the cable pay out rate and the ship ground speed in accordance with laying conditions, and the speed controller of the cable engine based on an $H^{infty}$ servo control is designed for adjusting the cable engine in order to lay a desired amount of slack. The controller is designed to have the robust tracking property of the cable engine under disturbances. The performance of the designed controller is evaluated by computer simulation, and, consequently, a feasibility study for laying the submarine cable stably is done through analyzing simulation results.