In an apparatus for controlling an outboard motor having an internal combustion engine to power a propeller, and a torque converter interposed between the engine and a drive shaft and equipped with a lockup clutch, it is configured to have a throttle opening detector that detects throttle opening of a throttle valve of the engine, a throttle opening change amount calculator that calculates a change amount of the calculated throttle opening, and a clutch ON unit that makes the lockup clutch ON when the calculated change amount is equal to or greater than a predetermined value, and keeps the lockup clutch ON during a predetermined time period. With this, it becomes possible to improve acceleration performance immediately after the engine speed is accelerated.