In group key management, the implementation of encryption often fails because multicast communication does not provide reliable linkage. In this paper, a new group key management scheme is proposed for multicast communication in fog computing networks. In the proposed scheme, any legal fog user belonging to a fog node will be able to decrypt a ciphertext encrypted by a secret shared key. The shared secret key is divided into key segments. In the rekeying operation process, each key segment is split into two factors with its shared production mechanism. The key updates are required to belong to the fog provider or the group management device. Fog users will have independent key segments unchanged. Then, the cost, the message of rekeying, and the dependence on credible channels will be decreased. This method can resist collusion attacks and ensure backward security and forward security, even if the number of users leaving is larger than the threshold value. Our scheme is also suitable for untrusted affiliate networks.