Home Energy Management Systems (HEMS) contain devices of multiple manufacturers. Also, a large number of groups of devices must be managed according to several clustering situations. Hence, since it is necessary to establish a common secret group key among group members, the group key management scheme of IEEE 802.21 is used. However, no security verification result by formal methods is known. In this paper, we give the first formal verification result of secrecy and authenticity of the group key management scheme of IEEE 802.21 against insider and outsider attacks using ProVerif, which is an automatic verification tool for cryptographic protocols. As a result, we clarify that a spoofing attack by an insider and a replay attack by an outsider are found for the basic scheme, but these attacks can be prevented by using the scheme with the digital signature option.