This paper investigates the fundamental covert rate performance in a wireless relaying system consisting of a source-destination pair, a full-duplex (FD) relay and a warden, where the relay can work at either the FD mode or the half-duplex (HD) mode. We first provide theoretical modeling for the instantaneous/average covert rate when the system works solely under the FD mode or HD mode, and then explore the corresponding optimal transmit power control of relay for the covert rate maximization. For an improvement of covert rate, we further propose a joint FD/HD mode that flexibly switches between the FD and HD modes depending on channel state of the relay self-interference channel. Under the joint FD/HD mode, we also examine the related problems of theoretical modeling for covert rate and optimal transmit power control of relay for covert rate maximization. Finally, extensive numerical results are provided to illustrate the covert rate performances of the relaying system under the FD, HD and joint FD/HD modes.