In recent years, wireless covert communication has emerged as an effective approach to concealing the very existence of a transmission from an eavesdropper (Willie), particularly through the use of relays. The level of covertness of the transmitter (Alice) depends on Willie’s detection error, and one of the most effective ways to increase this error is by employing artificial noise. However, increasing the noise power may degrade the received signal quality at the legitimate receiver (Bob). To address this issue, this paper proposes an adaptive method based on a full-duplex relay equipped with artificial noise generation capability. The relay adaptively adjusts its noise power according to the received power from Alice, thereby increasing Willie’s detection error while mitigating self-interference. Moreover, by time-splitting the transmission of data and noise, the harmful effect of noise on Bob is eliminated. Through rigorous mathematical analysis, the optimal maximum and minimum values of artificial noise power are derived. Simulation results, which verify the analytical findings, demonstrate that the proposed method improves Willie’s detection error by up to 35% and enhances the covert communication rate by up to 33% compared with existing schemes.