Broadcast encryption is the scheme that a sender encrypts messages for a designated group of receivers, and sends the ciphertexts by broadcast over the networks. Dynamic environment of broadcast encryption needs to support conditions which someone can join a group, members of a group can leave a group, a group can join other groups, and a group can be separated into smaller groups dynamically. In this paper, we propose a dynamic broadcast encryption scheme based on braid groups cryptosystem, which is an alternative method in the public key cryptosystem and can reduce the computational cost. Join, leave, merge, and partition protocols are stated in our scheme to deal with dynamic environment. Our scheme has some advantages over the scheme using symmetric group key in that the sender can be someone inside or outside the group and it gets rid of the problem in distributing a secret key.