In this study, we analyse the inventory management strategy for perishables, where customer demands are assumed to arrive continuously and modelled by a drifted Brownian motion. We apply the well-known (s, S) continuous review inventory policy; in this policy, an order is placed to increase the inventory level to S as soon as it falls below s. Benefitted from highly developed transportation and logistics industries, it is reasonable to employ the zero-leadtime assumption in our model. In addition, a buyback contract is granted for the retailer to recover the loss from perishing. We illustrate the sales cycle through Markov renewal approach and derive closed-form formulas for long-run profit rates. To evaluate the optimal ordering policy which maximises the profit rate of the retailer, we first analyse the condition for accepting backorder and derive the optimal backorder level s as a function of S, and then solve for the global optimal (s, S) policy through numerical studies. Moreover, we develop a heuristic approach to approximate the optimal policy. Sensitivity analyses are conducted to reveal the effect of different parameters on system behaviour. The conclusions provide managerial insights for formulating inventory policies for perishables under Brownian demand.