In covert communication systems, covert messages can be transmitted without being noticed by the monitors or adversaries. Therefore, the covert communication technology has emerged as a novel method for network authentication, copyright protection, and the evidence of cybercrimes. However, how to design the covert communication in the physical layer of wireless networks and how to improve the channel capacity for the covert communication systems are very challenging. In this paper, we propose a wireless covert communication system, where data streams from the antennas of the transmitter are coded according to a code book to transmit covert and public messages. We adopt a modulation scheme, named covert quadrature amplitude modulation (QAM), to modulate the messages, where the constellation of covert information bits deviates from its normal coordinates. Moreover, the covert receiver can detect the covert information bits according to the constellation departure. Simulation results show that proposed covert communication system can significantly improve the covert data rate and reduce the covert bit error rate, in comparison with the traditional covert communication systems.