Healthcare requires continuous and systematic innovation in order to provide high quality services. Cloud computing is a new model of computing that promises to provide more flexibility, less expense and more efficient IT services to end-users. Large amount of sensitive data is shared by the healthcare cloud users. Here, privacy and security of group sharing data have become two major issues. The aim of this paper is to propose a ternary tree based TGDH protocol for dynamic group data sharing in healthcare cloud that could be used by a healthcare organization to share their data in dynamically secure groups containing other health organizations. Secure and reliable group communication in healthcare organizations is an increasingly active research area by growing popularity in group oriented and collaborative applications. Ternary tree approach covers more other healthcare members (organizations) in a subgroup and height of ternary tree will get increase when number of members in a group increase where height of tree is number of iterations required to compute group shared key.