This work investigates the phase gain of intelligent reflecting surface (IRS) covert communication over complex-valued additive white Gaussian noise (AWGN) channels. The transmitter Alice intends to transmit covert messages to the legitimate receiver Bob via reflecting the broadcast signals from a radio frequency (RF) source, while rendering the adversary Willie’s detector arbitrarily close to ineffective. Our analyses show that, compared to the covert capacity for classical AWGN channels, we can achieve a covertness gain of value 2 by leveraging Willie’s uncertainty of phase angles. This covertness gain is achieved when the number of possible phase angle pairsN= 2. More interestingly, our results show that the covertness gain will not further increase withNas long asN≥ 2, even if it approaches infinity.