A key assignment scheme for a secure group communication system based on a geometric approach is proposed. Members obtain the group key by solving multiple linear equations, using both the public information on the notice board and the secret information of their own. The proposed scheme can be divided into three phases: user registration, group key assignment, and group key computation. In the user registration phase, the group controller computes and gives a secret to the new user based on geometric approaches. In the group key assignment phase, the group controller first constructs a secret circle using the group key. Then it computes a shadow of group key for each member based on the shared secret. Finally, each member obtains an additional secret point based on the shared secret. The member obtains the group key in the group key computation phase by its shadow and the public information. The experimental results show that the computation of this scheme is simple and fast. It is dynamic because not only initial key distribution, but also auxiliary operations, such as members joining, members leaving, the group key updating are implemented. The forward secrecy and backward secrecy are assured.