Some efficient broadcast authentication protocols have been proposed for wireless sensor networks. However, these protocols face the authentication delay problem, which is not suitable for the applications that needs quick response and hopbyhop authentication mechanisms. This paper concludes the protocols proposed for immediate authentication and points out that they actually turn the authentication delay from receivers to senders. This paper proposes a new fast broadcast authentication a protocol named FBAP (Fast Broadcast Authentication Protocol). FBAP is based on the loose demand on authentication delay. Through carefully configuration on a packet sending mechanism, the authentication delay of FBAP is limited to a threshold. It is concluded from analyses and performance evaluations that FBAP works well in more communication scenarios and has a smaller communication overhead than RPT and other protocols proposed before.