A controller of an automatic transmission having a lockup clutch and a control method of the automatic transmission, in which engine rotational speed is prevented from changing even though turbine rotational speed changes at gear shift and slip control can be carried out without making a driver feel uncomfortable are provided. When a speed change command is detected and it is determined that an inertia phase has not yet started, target engine rotational speed during a replenish period is calculated and the target engine rotational speed control is carried out to have the target engine rotational speed. When it is determined that the control is in the inertia phase, another target engine rotational speed during the inertia phase is calculated. Then, target engine rotational speed control in which the engine rotational speed at the start of the inertia phase is maintained as the target engine rotational speed is carried out.