In general, real-time video service is more sensitive to cell transmission delay than to cell loss. Existing handoff schemes emphasizing prevention of cell loss had limitations in cell transmission delay to satisfy QoS (Quality of Service). Thus, a scheme to minimize transmission delay generated during the handoff maintaining the sequence of cells is proposed. In this paper, transmission delay can be reduced by transmitting ATM cells with low CLP (CLP=0) prior to others and by discarding cells with high CLP (CLP=1). The proposed scheme is proven to be suitable for delay-sensitive real-time VBR service and appropriate for fast handoffs by giving high CLP (Cell Lose Priority) to less meaningful MPEG frames.