The present disclosure relates to a control method of a dual clutch transmission for a hybrid electric vehicle, and a control system for the dual clutch transmission. The control method includes: a handover step of performing a handover process of a transmission while controlling clutch torque of an engaging-side input shaft to maintain a rotational speed change rate of the engaging-side input shaft at a reference change rate; and an actual shifting step of synchronizing a rotational speed of a motor with a rotational speed of the engaging-side input shaft when the first finish determining step determines that the handover process has finished, and of increasing a rotational speed change rate of the motor by increasing motor torque when a synchronization rate is a reference synchronization rate or less.