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In this paper, we present an energy efficient priority-based MAC (EEP-MAC) protocol for energy harvesting Wireless Sensor Networks (WSNs). To provide priority-based data transmission the EEP-MAC uses the modified IEEE 802.15.4 beacon frame. A receiver node periodically wakes up, receives sender beacon frames from its neighbors, and broadcasts a beacon frame containing the selected sender's address. A receiver node selects sender node according to sender's data priority. Under EEP-MAC protocol, no hidden terminal problem can happen. We show the performance of EEP-MAC through simulations and analytical analysis, and compare it against the previous MACs. Results have shown that our protocol outperforms other MAC in terms of energy consumption, higher priority packet delivery delay.