A new approach in optical burst switching(OBS) networks with QoS support is presented in this paper. In the approach,the data channels of an outgoing link at a core node are divided into multiple groups,with each group corresponding to a service class. The number of data channels in each group is mainly determined by data traffic. In general,a data burst(DB) can be sent on a data channel reserved by its burst head packet(BHP) only in its own group. Upon failing to reserve any bandwidth in its own group,the BHP tries to re-reserve even preempted bandwidth on a data channel in a lower-priority group. A lower-priority BHP can't reserve bandwidth on any data channel in a higher-priority group. In addition,the reasonable relation between the preempting DB length and the preempted DB length is also investigated in this paper.