A speed change control system for reducing shift shocks of clutch-to-clutch shifting is provided. The control system is applied to a vehicle in which a transmission having engagement devices is connected to an output side of a prime mover, and in which a gear stage of the transmission is shifted among a plurality of stages by changing engagement states of the engagement devices. The speed change control system carries out a clutch-to-clutch shifting from a predetermined gear stage to another gear stage by reducing a torque capacity of the predetermined engagement device to be disengaged while increasing a torque capacity of another engagement device to be engaged. An output shaft torque calculation means calculates a target torque of an output shaft of the transmission on the basis of an input shaft torque of the transmission based on a drive demand, an angular acceleration of the input shaft, an angular acceleration of the output shaft, and a torque transmission ratios of the engagement devices to be engaged and to be disengaged. A torque capacity calculation means calculates a torque capacities of the engagement device to be engaged and to be disengaged during a torque phase and an inertia phase under the clutch-to-clutch shifting, on the basis of the target torque value of the output shaft, the angular acceleration of the input shaft, the angular acceleration of the output shaft, and the torque transmission ratios of the engagement devices to be engaged and to be disengaged.