In recent years, the conventional degrees of freedom in frequency and time have been fully used. It is difficult to further improve the performance of communication systems with such degrees of freedom. Orbital angular momentum (OAM), which provides a new degree of freedom for millimeter-wave (mmWave) wireless communication systems, has been recognized as a key enabling technique for future mobile communication networks. By combining OAM beams that have theoretically infinite and mutually orthogonal states with the generalized spatial modulation (GSM) strategy, a new OAM-GSM mmWave wireless communication system is designed in this paper. A bit error rate (BER) model of the OAM-GSM system is established based on channel flip precoding. The channel capacity, energy efficiency, and BER of the proposed OAM-GSM mmWave wireless communication system are simulated. Numerical results show that, compared with traditional GSM systems, the OAM-GSM system has more complex transmission and reception mechanisms but the channel capacity and maximum achievable energy efficiency are increased by 80% and 54%, respectively, and the BER drops by 91.5%.