A control device for an automatic transmission of a vehicle arranged to bring a torque converter to a lockup state and to perform a fuel cut by which a fuel supply to an engine is stopped during a coast traveling in which an accelerator pedal is released, to release the lockup of the torque converter when an engine speed (Ne) is decreased to a lockup release rotation speed (N Lure) during the fuel cut, and to perform a fuel recovery to finish the fuel cut to restart of the fuel supply to the engine when the engine speed (Ne) is decreased to be a fuel recovery rotation speed (N FCR) lower than the lockup release rotation speed (N Lure), the automatic transmission including the torque converter, and a stepwise automatic shift mechanism to which a rotation from the engine is input through the torque converter, and which is arranged to attain a plurality of shift stages by combinations of engagements and disengagements of a plurality of frictional engagement elements, the control device comprising: a shift control means configured to perform a downshift control of the automatic shift mechanism by a changeover of the frictional engagement elements when a vehicle speed (Vsp) is decreased to be equal to or smaller than a predetermined downshift vehicle speed (Vd) during the fuel cut, characterized in that the shift control means includes; a deceleration state judging section configured to judge whether a deceleration (Gd) of the vehicle is a gentle deceleration state or a sudden deceleration state, and a downshift control section configured to command a plural stage downshift to downshift from a current shift stage of the automatic shift mechanism to a target shift stage that is lower than the current shift stage by two stages or more when the deceleration state judging section judges the sudden deceleration state, wherein the plural stage downshift includes a continuous downshift to continuously downshift through an intermediate shift stage toward the target shift stage, and wherein the shift control means is configured to judge the shift based on a shift judgement vehicle speed value (Vpr) based on the detected vehicle speed (Vsp) and the deceleration by using a shift map in which shift lines are set, and to judge the shift by shifting the shift judgement vehicle speed value (Vpr) to a lower speed side when the continuous downshift is performed. to bring a torque converter to a lockup state and to perform a fuel cut by which a fuel supply to an engine is stopped during a coast traveling in which an accelerator pedal is released, to release the lockup of the torque converter when an engine speed (Ne) is decreased to a lockup release rotation speed (N Lure) during the fuel cut, and to perform a fuel recovery to finish the fuel cut to restart of the fuel supply to the engine when the engine speed (Ne) is decreased to be a fuel recovery rotation speed (N FCR) lower than the lockup release rotation speed (N Lure), the automatic transmission including the torque converter, and a stepwise automatic shift mechanism to which a rotation from the engine is input through the torque converter, and which is arranged to attain a plurality of shift stages by combinations of engagements and disengagements of a plurality of frictional engagement elements, the control device comprising: a shift control means configured to perform a downshift control of the automatic shift mechanism by a changeover of the frictional engagement elements when a vehicle speed (Vsp) is decreased to be equal to or smaller than a predetermined downshift vehicle speed (Vd) during the fuel cut, characterized in that the shift control means includes; a deceleration state judging section configured to judge whether a deceleration (Gd) of the vehicle is a gentle deceleration state or a sudden deceleration state, and a downshift control section configured to command a plural stage downshift to downshift from a current shift stage of the automatic shift mechanism to a target shift stage that is lower than the current shift stage by two stages or more when the deceleration state judging section judges the sudden deceleration state, a shift control means configured to perform a downshift control of the automatic shift mechanism by a changeover of the frictional engagement elements when a vehicle speed (Vsp) is decreased to be equal to or smaller than a predetermined downshift vehicle speed (Vd) during the fuel cut, characterized in that the shift control means includes; a deceleration state judging section configured to judge whether a deceleration (Gd) of the vehicle is a gentle deceleration state or a sudden deceleration state, and a downshift control section configured to command a plural stage downshift to downshift from a current shift stage of the automatic shift mechanism to a target shift stage that is lower than the current shift stage by two stages or more when the deceleration state judging section judges the sudden deceleration state, wherein the plural stage downshift includes a continuous downshift to continuously downshift through an intermediate shift stage toward the target shift stage, and wherein the shift control means is configured to judge the shift based on a shift judgement vehicle speed value (Vpr) based on the detected vehicle speed (Vsp) and the deceleration by using a shift map in which shift lines are set, and to judge the shift by shifting the shift judgement vehicle speed value (Vpr) to a lower speed side when the continuous downshift is performed.