To broadcast a message secretly and consistently to the receivers in the broadcasting networks, Jeong et al. suggested an efficient secret broadcast scheme using binding encryption quite recently. In this letter, we first show that their scheme just achieves consistency in a relatively weak security model but not in a stronger model. Furthermore, we point out their scheme is not so efficient even when their model is accepted. Thereafter, we suggest a simple and more efficient scheme, which can be proved in their model without using random oracles.