A control device (12) for a stepped transmission mechanism 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 a vehicle is stationary was satisfied and before a stop of an engine (1). The control device includes a gradient detecting section (12a, 47) that detects a gradient (R) of a road surface on which the vehicle is stationary; and a hydraulic control section (12c) that performs a slipping interlock by reducing the hydraulic pressure to a second predetermined pressure (P2), if the gradient R detected by the gradient detecting section is lower than or equal to a predetermined value (RTH) during the interlock and before the stop of the engine.