Many research works have been conducted in the preventive maintenance area since maintenance strategies have become more and more significant in industry and supply chain services. However, previous studies are mainly based on age maintenance policies and other multi-criteria approaches instead of Multi-Attribute Utility Theory (MAUT). There are some studies proposed by using MAUT, but they assume that the maintenances are perfect. This paper presents an imperfect maintenance model of a one-unit system to obtain an optimal inspection interval based on MAUT. The proposed model is designed to identify the systems' status by making a trade-off between cost attribute and reliability attribute. By taking decision makers' preferences into account, with the assumption of imperfect maintenance, the model receives a result of an optimal inspection interval. This model is applicable for equipment or systems that suffer graded failures and can be repaired at any time during the operation. A numerical application is given to illustrate that with consideration of decision-makers' priorities, the model can provide new solutions for imperfect maintenance interval optimization, which is a suggestion for future research.