In the inventory model, people usually assume that the inter-demand times are independent and identically distributed, but that may not be true in reality. This limitation motivated us to seek greater understanding of an important class of inventory models with dependent demand. In this paper we analyze an ( , Ss ) continuous review perishable inventory system with a Markovian renewal demand process. Using a Markovian renewal approach, we derive the transition matrix and some performance measures of the system. We then construct a closed-form expected cost function showing some managerial insights on controlling such inventory systems.