A shift control apparatus for controlling an automatic transmission of a motor vehicle having an engine, said transmission having a plurality of operating positions and including two hydraulically operated frictional coupling devices one and the other of which are released and engaged, respectively, to effect a clutch-to-clutch shift of said transmission from one of said operating positions to another of said operating positions, said shift control apparatus comprising (a) excessive engine speed preventing means for preventing a rise of a speed of said engine above an upper limit, (b) hydraulic control means for regulating hydraulic pressures of said two frictional coupling devices such that an amount of overshoot of said speed of the engine is held within a predetermined range during a period of said clutch-to-clutch shift, and (c) overshoot control means for compensating at least one of said hydraulic pressures as regulated by said hydraulic control means, when said amount of overshoot of the speed of said engine is outside said predetermined range, said shift control apparatus further comprising:
- engine state detecting means for detecting an operating state of said engine during said clutch-to-clutch shift of said transmission;
- and
- inhibiting means for inhibiting an operation of said overshoot control means, if said operating state of said engine detected by said engine state detecting means is expected to cause activation of said excessive engine speed preventing means during said clutch-to-clutch shift of said transmission.