Distributed online social network (DOSN) solves the challenges of single-point failure and user data privacy faced by traditional online social network (OSN). Online discussion group, allowing a user to facilitate the communications with other users, is one of the most important components of (D)OSN. Key management is the key technology to ensure the secure establishment of discussion groups in DOSNs. However, the existing key management schemes for secure discussion group establishment in DOSNs cannot meet the requirements of sender non-restriction, receiver controllability, round optimal, certificate freeness simultaneously. In this paper, we propose a novel key management scheme for secure discussion group establishment in DOSNs. In our scheme, any user could use our key management scheme to initialize a discussion group with a piece of discussion group information. Users who are interested in the group topic contained in the discussion group information can join and leave the discussion group at any time once the discussion group is initialized with one-round communication. Any user/sender can find the users that he/she wants to communicate with by looking up the discussion group information of a discussion group and then send encrypted messages to some or all of the users in the discussion group. Therefore, our scheme achieves sender non-restriction, receiver controllability, round optimal, certificate freeness simultaneously. Security analysis also shows that our scheme achieves confidentiality, authentication, full collusion resistance, known-key security and perfect forward security.