Motivated by the need to reduce the maintenance cost and improve the system reliability, the issue of selective maintenance has attracted much attention in the industrial and military fields. The existing research mainly focused on binary-state systems or the perfect maintenance strategy. In this paper, we presented a novel selective maintenance model for multi-state deteriorating systems with multi-state components considering imperfect maintenance strategy. The proposed model aims to minimize the total maintenance costs and takes the relationship between the maintenance cost, the system service life and the maintenance quality into account. A case study where the proposed model was applied to an aircraft gas turbine engine system was conducted. The sensitivity analyses for the minimum requirement of the health level, the aging factor, and the number of health states were conducted, respectively. Moreover, a comparative analysis between perfect and imperfect maintenance strategies was conducted, and the results demonstrated that the imperfect maintenance strategy was more cost-effective than perfect maintenance strategy. The findings of this study can guide the maintenance decision-making process for actual systems.