In an apparatus for controlling operation of an outboard motor having an internal combustion engine and transmission, it is configured to determine whether acceleration is instructed to the engine by an operator when the gear position is the second speed, detect a slip ratio of a propeller based on theoretical velocity and actual velocity of a boat, control a throttle opening to suppress increase in the slip ratio when the acceleration is determined to be instructed, and change the gear position from the second speed to the first speed when the slip ratio is equal to or less than a first predetermined value and the change amount of the slip ratio is equal to or less than a prescribed value. With this, it becomes possible to appropriately control operation of the engine and the transmission during acceleration, thereby improving the acceleration performance of immediately after acceleration start.