In cloud computing environment, resources are accessed by multiple members. Resources may be considered as VM, CPU, Storage etc. Group key management required when multiple members in group accesses the resources securely. In existing group key management, separate key trees are formed even if members are common in another group to access the resources. The solution to this is to form the combined key trees for resources which containing overlapping members. Through the analysis it is observed that computational overhead is decreased by 22% if we combine the key trees than separate key trees for each resource.