In an outboard motor steering system, the engine speed is detected as a value indicative of the speed of the boat and a current value for operating a steering hydraulic cylinder is determined to decrease with decreasing engine speed. The current value can therefore be determined in accordance with the steering load to reduce electric power consumption. Moreover, owing to the fact that the drive current is determined as a function of steering load, it is possible to prevent the output of the cylinder from becoming excessive relative to the steering load, thereby ensuring that the steered angle tracks a desired steering angle with good accuracy.