In relation to an automatic transmission which has a plurality of friction engagement devices that are engaged when supplied with oil pressure and which establishes a plurality of speed change steps in accordance with engaged and released states of the friction engagement devices, a control device of a vehicular automatic transmission that switches between the speed change steps in accordance with a predetermined shift rule includes a controller which changes the shift rule to an air discharge-purpose shift rule that is set so as to provide a higher probability of switching to a speed change step that involves engagement of a predetermined friction engagement device of the friction engagement devices than the shift rule in order to discharge air that has intruded in a hydraulic circuit of the predetermined friction engagement device, and which causes switching between the speed change steps in accordance with the air discharge-purpose shift rule.