A system for controlling a hybrid electric vehicle includes a control unit for determining whether or not an Oil Pump Unit (OPU) and an Electric Oil Pressure (EOP) temperature sensor are normally operated; a phase current density comparison unit for comparing the mean density of phase currents acquired after shifting the gears of the vehicle with the density of coil phase currents which flow through a coil at a maximum permissible temperature at which the coil is not burning; and a torque control unit for controlling the value of torque to be applied to a transmission according to a result acquired by the phase current density comparison unit.