The use of wireless sensor networks (WSNs) is growing up in the last few years. Therefore, new challenges arise every day and one of the emerging challenges in WSNs is the nodes mobility support. This feature increases the application areas of these technologies but also raises new challenges to solve. This paper proposes a new handover mechanism, called Hand4MAC (Handover mechanism for MAC layer supporting continuous communication in mobile wireless sensor networks), to deal with body sensors mobility in scenarios where patients are hospitalized. This approach tries to provide continuous monitoring and communication with these sensor nodes when they move across different access points wireless coverage range. The proposed method for medium access control (MAC) layer considers that nodes remain within the same network. The evaluation study of the proposed algorithm was performed by simulation and evaluated in comparison with the well-known RSSI-based handover algorithm. It was concluded that Hand4MAC performs better and reveals promising results for real deployment.