A shift control apparatus of an automatic transmission may include a data detector configured to detect driving data to perform a shift control, and a vehicle controller configured to determine a shift gear stage based on the driving data and control a transmission based on the shift gear stage, in which the vehicle controller sets driver's demand acceleration based on the driving data, sets a gear stage range which arrives at the driver's demand acceleration, and sets a target gear stage, at which fuel consumption is minimized, in the gear stage range to instruct a shift.