PURPOSE: To soften the speed change shock in up shift by outputting two kinds of control signals for turning-ON/OFF two kinds of solenoids installed on an automatic transmission and carrying out the shift between the first - fourth speed in four kinds of combinations of turning-ON/OFF.

CONSTITUTION: It is judged by map calculation if the shift variation demand exists or not, and if the judgement is 'YES', the speed change outputs C1 and C2 are changed immediately in case of down shift. In case of up shift, the variation rate TA of the throttle opening degree is compared with a certain value, and if TA is less than this value, it is judged that the throttle opening degree is sharply reduced, and further it is judged if a perfect throttle closing state (idle switch ON) state is generated or not. A certain time is set on a delay timer DELAY in the perfect closure state, and count is started after the lapse of a certain time after, the perfect closure. After the completion of the DELAY timer, the speed change outputs C1 and C2 are changed for the prescribed up shift. Accordingly, the number of revolution of the engine lowers during this shift, and the speed change shock is softened.