A control device for a transmission mechanism for controlling a stepped transmission mechanism which includes a first clutch to be engaged at startup and a second clutch different from the first clutch and is interlocked when a hydraulic pressure is supplied to the first clutch and the second clutch and the first clutch and the second clutch are completely engaged, comprising: hydraulic pressure control means adapted to control a hydraulic pressure supplied to the stepped transmission mechanism so that the first clutch is set in a completely engaged state and the second clutch is set in a slip interlock state where the second clutch is not completely engaged in the case of a return from an idle stop control in which an engine is automatically stopped, characterized in that the hydraulic pressure control means: - includes target output torque calculation means adapted • to calculate an input torque of the stepped transmission mechanism based on an engine rotation speed, and • to calculate a target output torque of the stepped transmission mechanism based on • a target output torque of the stepped transmission mechanism calculated last time and stored in a memory device; • a deviation between the input torque of the stepped transmission mechanism, and an input torque of the stepped transmission mechanism calculated last time and stored in the memory device; and • a minimum increased amount of a target output torque with which a feeling of slowness at startup is not given to the driver and a shock given to the driver decreases, the minimum increased amount of the target output torque being set according to a gradient of a road surface in a traveling direction of a vehicle; and - controls the hydraulic pressure supplied to the second clutch based on the target output torque calculated by the target output torque calculation means. - includes target output torque calculation means adapted • to calculate an input torque of the stepped transmission mechanism based on an engine rotation speed, and • to calculate a target output torque of the stepped transmission mechanism based on • a target output torque of the stepped transmission mechanism calculated last time and stored in a memory device; • a deviation between the input torque of the stepped transmission mechanism, and an input torque of the stepped transmission mechanism calculated last time and stored in the memory device; and • a minimum increased amount of a target output torque with which a feeling of slowness at startup is not given to the driver and a shock given to the driver decreases, the minimum increased amount of the target output torque being set according to a gradient of a road surface in a traveling direction of a vehicle; and • to calculate an input torque of the stepped transmission mechanism based on an engine rotation speed, and • to calculate a target output torque of the stepped transmission mechanism based on • a target output torque of the stepped transmission mechanism calculated last time and stored in a memory device; • a deviation between the input torque of the stepped transmission mechanism, and an input torque of the stepped transmission mechanism calculated last time and stored in the memory device; and • a minimum increased amount of a target output torque with which a feeling of slowness at startup is not given to the driver and a shock given to the driver decreases, the minimum increased amount of the target output torque being set according to a gradient of a road surface in a traveling direction of a vehicle; and • a target output torque of the stepped transmission mechanism calculated last time and stored in a memory device; • a deviation between the input torque of the stepped transmission mechanism, and an input torque of the stepped transmission mechanism calculated last time and stored in the memory device; and • a minimum increased amount of a target output torque with which a feeling of slowness at startup is not given to the driver and a shock given to the driver decreases, the minimum increased amount of the target output torque being set according to a gradient of a road surface in a traveling direction of a vehicle; and - controls the hydraulic pressure supplied to the second clutch based on the target output torque calculated by the target output torque calculation means.