A control device for an automatic transmission for a vehicle including a torque converter interposed between an output shaft of an engine and an input shaft of the automatic transmission, the torque converter having a lock-up clutch for mechanically connecting the output shaft and the input shaft in a direct manner, and a lock-up clutch engagement control unit for engaging the lock-up clutch by a predetermined engagement force in a predetermined operational region determined by a throttle angle and a vehicle speed. The control device further includes a shift map having a slip region for the lock-up clutch set in relation to a plurality of shift characteristics preliminarily set according to vehicle speeds, the slip region being defined by a downshift line and a slip start line deviated from the downshift line by a predetermined range of throttle angle toward lower throttle angles. When the throttle angle falls within the slip region before kickdown, the slip control of the lock-up clutch is performed by the lock-up clutch engagement control unit.