A relay device is provided for relaying communication between a radio base station and a communication terminal, which includes a relay function management unit to switch on or off a relay function for relaying communication between the radio base station and the communication terminal, and a change command transmission unit to transmit, to the communication terminal, a change command of a handover threshold for the communication terminal which has established a wireless communication connection with the relay device in a case where the relay function management unit switches off the relay function.