This study investigates a closed-loop supply chain (CLSC) inventory model consisting of a retailer, a manufacturer and a supplier. Here, the return rate is considered to be varied which depends upon the quality level of returned items. The manufacturer performs manufacturing and remanufacturing processes to satisfy the retailer's demand. The manufacturing process is assumed to be imperfect and produces some defective items. All defective items are then reworked. Two recovery processes are considered in the model, which are remanufacturing and refurbishing. The recoverable items which cannot be perfectly recovered will be categorised as refurbishable items and then sold to the secondary market at a reduced price. A solution methodology is provided to find the optimal solutions of the model. A numerical example and sensitivity analysis are performed to show the application of the model and to understand the effects of the changes in key parameters on the model's behaviour, respectively.