In an apparatus for controlling an outboard motor mounted on a stern of a boat and having an internal combustion engine to power a propeller, a drive shaft that connects the engine and the propeller, and a torque converter that is interposed between the engine and the drive shaft and is equipped with a lockup clutch, it is configured to have a planing determiner that determines whether the boat is planning and a clutch ON unit that makes the lockup clutch ON when the boat is determined to be planing. With this, it becomes possible to appropriately make the lockup clutch ON after completing acceleration, thereby improving speed performance.