Nowadays, fierce competition and increasing customer requirements force manufacturers to continuously provide better after-sales services and supports. One such kind of after-sales services is product warranty which has been offered for almost all products in today's market. In this paper, we study a new warranty policy, called piece-wise renewing free replacement warranty. Under this policy, the whole warranty period is divided into two sub-periods and once an item fails in a specific sub-period, it will be replaced by a new identical one and the warranty period is fully or partially renewed. The expected warranty cost and warranty cycle of this policy are derived from the manufacturer's perspective. The proposed model is then modified by involving three sub-periods and a failure limit, respectively. In the latter scenario, when the number of item failures over a warranty cycle exceeds a pre-specified threshold, the manufacturer has to refund the item's purchase price, and consequently the warranty ceases. A real-world case study is presented using warranty data of a battery manufacturer. It is found that for a given warranty period, the piece-wise renewing free replacement policy has a better performance than traditional fully renewing policy, in terms of expected warranty cost, warranty cycle, and cost rate.