A flexible duct is connected between the outboard motor and the hull transom, to supply air, fuel, power and control cables to the motor liftably and steerably attached to the transom, even when the motor sinks into water. To improve the durability of the flexible duct, that is, to allow the flexible duct not to be moved whenever the outboard motor is pivoted for steering operation, the air supply apparatus for an outboard motor comprises (a) a hollow steering shaft pipe fixedly supported near the transom; (b) upper and lower bearings, attached between the steering shaft pipe, for supporting the pivotal steering shaft of the motor; (c) a cylindrical cover for pivotably and slidably covering the upper end of the steering shaft pipe; and (d) a flexible duct connected between the transom and the fixed hollow steering shaft pipe.