How to ensure privacy security and improve computing efficiency is a research hotspot in the field of machine learning. Among them, how to balance the interests of users, cloud servers and attackers on the premise of ensuring user privacy is a difficult problem in the field of machine learning privacy protection. The development of quantum computing breaks through the computational bottleneck of classical machine learning and has derived the research direction of quantum machine learning. At present, hybrid quantum classical machine learning in NISQ era has become a research hotspot, but researchers rarely pay attention to the privacy protection in quantum machine learning. Therefore, this paper is the first to apply game theory to the privacy protection in quantum machine learning and proposes the privacy game model of user - server - attacker in Hybrid Classical Quantum BP Neural Network (HCQBPNN). Different from previous studies, this paper sets game strategies based on users' privacy requirements in practical applications, and aims to maximize the interests of attackers, cloud servers and users. The experiment proves that users can use the privacy game model proposed in this paper to get the optimal privacy combination strategy, and at the same time make the cloud server and the attacker can obtain positive income.