Cognitive radio communication can opportunistically access underutilized spectrum for emerging wireless applications. With interweave cognitive implementation, a secondary user (SU) transmits only if primary user does not occupy the channel and waits for transmission otherwise. Therefore, secondary packet transmission involves both transmission periods and waiting periods. The resulting extended delivery time (EDT) is critical to the throughput analysis of secondary system. In this paper, we study the EDT of secondary packet transmission with adaptive modulation under interweave implementation to facilitate the delay analysis of such cognitive radio system. In particular, we propose an analytical framework to derive the probability density functions of EDT considering random-length SU transmission and waiting periods. We also present selected numerical results to illustrate the mathematical formulations and to verify our analytical approach.