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Recently, several group password-authenticated key exchange (GPAKE) protocols have been proposed, Byun and Wang et al also proposed different passwords group PAKE protocols successively, and the clients in their protocols were all in the same realm. However, in practice we also need to establish a secure communication channel between groups who are in different realms. So, we proposed a cross-realm group PAKE protocol using different passwords. The proposed protocol extends Wang's GPAKE protocol from single realm to two realms, it enables groups in different realms to agree on a common group session key with the help of servers. We also gave the security analysis and computational costs for our protocol.