This paper investigates how to characterize the effect of multiple spectrum handoff delay on the extended data delivery time of the secondary users' connections in cognitive radio (CR) networks. Whenever a primary user appears, the spectrum hand-off procedures are initiated for the interrupted secondary users. Through spectrum sensing, the secondary user can reactively decide the target channel for spectrum handoff to resume its unfinished transmission. Clearly, many interruptions from the primary users will result in multiple handoffs, thereby increase the extended data delivery time of a secondary connection. In this paper, we develop a Markov transition model integrating with the preemptive resume priority (PRP) M/G/1 queueing network to characterize the multiple handoff delay, resulting from the sensing time, the handshaking time, the channel switching time, and the waiting time. The analytical results can facilitate the designs of admission control rules for the secondary users subject to their latency requirements and provide a framework to determine whether the spectrum sensing technology can effectively shorten the extended data delivery time under various traffic arrival rates and service time as well as sensing time1.