In recent years, channel-hopping based medium access control (MAC) protocols are proposed to improve the capacity in a decentralized multi-channel cognitive radio (CR) networks without extra usage of a control channel. Each CR user has to stochastically follow a default channel-hopping sequence in order to sense a channel and to conduct its frame transmission. In this paper, based on the channel-hopping protocol, an analysis is conducted on both the probability of channel availability and the average frame delay for the primary queueing networks. The analytical model is proposed by considering the impact caused by imperfect sensing of the CR users and the imperfect synchronization between the primary and CR networks. According to the proposed model with more realistic considerations, an optimal channel-hopping sequence (OCS) approach is designed for the CR users based on dynamic programming technique. It is designed by exploiting the optimal load balance between both the channel availability and channel utilization within the delay constraints of primary users (PUs). By adopting the OCS approach, the maximum aggregate throughput of CR users and the quality of service (QoS) requirement of PUs can both be achieved. Numerical results illustrate that the proposed OCS scheme can effectively maximize the aggregate throughput compared to conventional channel-hopping sequences, and as well guarantee the QoS requirement of the PUs.