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.