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This paper studies average waiting time analysis of opportunistic access in multi-channel cognitive radio networks with a single secondary user and multiple primary users by applying the M/G/1 preemptive priority queueing scheme. By employing convex optimization tool, the secondary user finds the optimal way to distribute the packets to all channels in the system. For sensitive delay network, we proposed an algorithm to distribute the secondary user's packets to the only group of channels which satisfy the delay constraint. Simulation are used to validate the results, and simulation results demonstrate a high degree of accuracy for the derived expressions. Results indicate that the performance of the secondary user depends on the data traffic characteristics of the primary users and also the delay constraint of the secondary user.