System and method for controlling mountain running of an electric vehicle

Disclosed is a system and method that controls an electric vehicle to apply a brake and output a torque of an engine, after completely stopping an electric vehicle on a slope by the brake and controlling the torque of the engine to be 0 when the torque of the motor has a positive value and the speed of the motor has a negative value when the electric vehicle rolls downhill during hill climbing, so that the safety and reliability of the electric vehicle can be improved when the electric vehicle is on a Slope uphill.