Many broadcast encryption schemes have been proposed for conventional networks. However, those schemes are not suitable for wireless sensor networks, which have very limited resources such as communication, computation, and storage. In this paper, we propose an efficient and practical identity-based broadcast encryption scheme for sensor networks by exploiting the characteristics of sensor networks: in the deployment stage, the set of neighboring sensor nodes are determined and most communications are conducted among the neighbors due to radio power limitations of the nodes. The proposed scheme features the following achievements: (1) all of the public keys and private keys are of constant size; (2) it satisfies all the security requirements for sensor networks. The proposed scheme is optimal in the sense that it requires no pairing operation when adopting pre-computation.