In this study, we propose an integrated inventory model, which is under fuzzy demand condition. Additionally, we consider maintenance in the model. There are two types of preventive maintenance, namely perfect preventive maintenance and imperfect preventive maintenance. If failure occurs, the minimal repair can restore the system to working order. During the competitive market today, the inventory policy is an important issue to the supply chain management. Therefore, the purpose of this paper is to build an integrated inventory model with minimal repair in a fuzzy environment to reflect real world situation. Numerical examples are given to illustrate the application of the model.