The broadcast operation, as a fundamental service in mobile ad hoc networks (MANETs), is prone to the broadcast storm problem if forwarding nodes are not carefully designated. The objective of reducing broadcast redundancy while still providing high delivery ratio under high transmission error rate is a major challenge in MANETs. In this paper, we propose a simple broadcast algorithm, called double-covered broadcast (DCB), which takes advantage of broadcast redundancy to improve the delivery ratio in an environment that has rather high transmission error rate. Among the 1-hop neighbors of the sender, only selected forwarding nodes retransmit the broadcast message. Forwarding nodes are selected in such a way that 1) the sender's 2-hop neighbors are covered and 2) the sender's 1-hop neighbors are either forwarding nodes or nonforwarding nodes covered by at least two forwarding neighbors. The retransmissions of the forwarding nodes are received by the sender as the confirmation of their reception of the packet. The nonforwarding 1-hop neighbors of the sender do not acknowledge the reception of the broadcast. If the sender does not detect all its forwarding nodes' retransmissions, it will resend the packet until the maximum number of retries is reached. Simulation results show that the proposed broadcast algorithm provides good performance under a high transmission error rate environment.