A control apparatus of a hybrid electric vehicle includes: a clutch provided between an engine and a motor generating power; a transmission serially connected to the motor; a driving information detector detecting driving information including an output speed of the motor, an output speed of the transmission, and a rotation speed of a driving shaft serially connected to the transmission; and a controller limiting an input torque of the motor or an input speed of the motor to a predetermined level or less when a difference between the output speed of the motor and the output speed of the transmission detected by the driving information detector is higher than a predetermined value. As a result, it is possible to prevent a hybrid electric vehicle from starting at an unwanted speed.