This paper proposes a novel scheme based on minimum delay at the edges (MDE) for optical burst switching (OBS) networks. This scheme is designed to overcome the long delay at the edge nodes of OBS networks. The MDE scheme features simultaneous burst assembly, channel scheduling, and pre-transmission of control packet. It also features estimated setup and explicit release (ESXR) signaling protocol. The MDE scheme can minimize the delay at the edge nodes for data packets, and improve the end-to-end latency performance for OBS networks. In addition, comparing with the conventional scheme, the performances of the MDE scheme are analyzed in this paper.