Burst retransmission can reduce data loss in burst contention in optical burst switching (OBS) core nodes. However, uncontrolled burst retransmission may significantly increase the network load and data loss probability, defeating the purpose of retransmission. Therefore, controlled retransmission should be studied to achieve reasonable retransmission, particularly to support quality of service (QoS) in OBS networks in which priority traffic exists. In this paper, we develop a QoS-supported controlled retransmission scheme in OBS networks. Different from previous works in the literature, we set a different value for the retransmission probability at each contention for both high-and low-priority bursts, set different retransmission probabilities for bursts of different priorities for QoS support, and propose a retransmission analytical model for OBS networks. We take into account the load at each link due to both the fresh and the retransmitted traffic and calculate the path-blocking probability and the burst loss probability for high-priority and low-priority bursts to evaluate the network performance. An extensive simulation is proposed to validate our analytical model.