Mobile sinks in wireless sensor networks have been the target of extensive research recently due to their efficient energy consumption and various possible applications. To support mobile sinks, an energy efficient routing protocol is essential. In this light, the present study proposes a milestone-based predictive routing protocol that improves energy efficiency. This study introduces the concept of a milestone node, which plays a role of spreading the estimated sink's future location information to the nodes located in the vicinity of the recent trail of the sink, and by using this information, nodes can route data packets to the mobile sink efficiently. Along with the proposed predictive routing protocol, this study also suggests a periodic broadcast scheme to provide the sink's location information to the entire network in order to increase the data packet delivery ratio. Simulation results show that the proposed routing protocol reduces energy consumption while maintaining high data packet delivery ratios compared to previous routing protocols such as ALURP and Elastic.