Two problems existing in highway vehicular ad hoc networks (VANET), i.e., the slow reaction problem (SRP) and the local broadcast storm problem (LBSP), are investigated. In SRP, a candidate forwarder (CF) close to a sender always rebroadcasts a packet with a low probability or rebroadcasts a packet after a long delay in sparse network, while LBSP occurs when vehicles contending for accessing channel in a local dense network. To solve these problems, a Sender-designated Opportunistic Broadcast Protocol (SOBP) is proposed, which has multiple CFs to broadcast packets and is irrelevant to node density. A sender designates a fixed number of CFs and assigns priorities to them before broadcasting a packet so that possible collisions in the receivers are avoided. To enhance the efficiency of a single transmission, the sender chooses the CFs separated with a certain distance to alleviate the effect of hidden node. The average number of transmissions in a successful broadcast is analyzed and the retransmission strategy to enhance the reliability is presented. One of the main features of SOBP is that it is able to keep broadcasting overhead at a low level. Simulations show that SOBP is able to effectively solve the SRP and the LBSP.