A control device (12) for a stepped transmission mechanism, the control device being mounted in a vehicle having an idle stop function, wherein the control device is configured to perform an interlock by engaging a first clutch (32) and increasing hydraulic pressure of a second clutch (33) up to a first predetermined pressure (P1) such that an output shaft of the transmission mechanism is fixed, after an idle-stop condition including at least a requirement that the vehicle is stationary was satisfied and before a stop of an engine (1), the first clutch (32) is configured to be used for a movement start of the vehicle, and the second clutch is provided separately from the first clutch, the control device comprising: a gradient detecting means (12a, 47) that detects a gradient (R) of a road surface on which the vehicle is stationary; and a hydraulic control means (12c) that performs a slipping interlock such that a slipping state is realized by reducing the hydraulic pressure to a second predetermined pressure (P2) which is lower than the first predetermined pressure (P1), if the gradient R detected by the gradient detecting means (47, 12a) is lower than or equal to a predetermined value (R TH ) during the interlock and before the stop of the engine (1).