As the IEEE 802.11 wireless local area networks (WLANs) have become very popular and the emerging IEEE 802.16e wireless metropolitan area networks (WMANs) also attract a great deal of attentions, in the future we can expect the appearance of the hybrid IEEE 802.11 WLANs and IEEE 802.16e WMANs systems. Clearly, seamless handoffs in this hybrid network will become an increasingly important issue. However, the system which has shortest handoff latency may not always have the highest throughput. In this paper, we develop a dynamic network selection scheme to determine the connecting system in a new "WLAN to hybrid WLAN/WiMax" handoff scenario, in which we consider both the vertical and horizontal handoffs. The proposed scheme requests the station to wait an additional network selection time "tw" before the selection to maximize the amount of delivered bits during a dwelling time. We also formulate an optimization problem to find the optimal network selection time tw* and show that the proposed scheme can improve the delivered information bits during handoff.