An outboard motor hydraulic mechanism having a hydraulic actuator moving the outboard motor about a rotary shaft relative to a boat the motor is mounted on and a hydraulic pump and a plurality of electric motors connected to the pump. A number of the motors to be operated is determined based on an estimated load acting on the actuator, output shafts of the motors are aligned coaxially with a drive shaft of the pump, and they are directly connected with each other. This ensures that the operator is prevented from having an unpleasant feeling, lowers electric power consumption by the motors, and reduces the number of components and simplifies the structure of the mechanism.