A system for controlling acceleration torque of a vehicle includes: a driving information detection unit that detects driving information of the vehicle; a forward-vehicle detector that detects the information about another vehicle located substantially ahead of the vehicle; and a control unit that calculates a basic acceleration torque and a basic slew rate of the vehicle when the vehicle is accelerating based on the detected driving information, calculates a desired acceleration torque and a final slew rate by correcting the basic acceleration torque and the basic slew rate based on the detected information about the other vehicle, and outputs a torque-related order to adjust a torque output from a power system of the vehicle to the desired acceleration torque in accordance with the final slew rate.