This paper proposes a contention resolution scheme considering multicast traffic in optical burst switching (OBS) networks. In OBS networks, for unicast bursts, contention can be avoided by deflection routing. However, deflection routing cannot be applied to multicast bursts because multicast bursts are transmitted along light-trees which are fixed, tree-shaped routes. Therefore, the loss probability of multicast bursts is generally high. To resolve this problem, the proposed scheme introduces an ingenious offset time assignment strategy which completely avoids contention of multicast bursts due to transmissions of unicast bursts by strategically assigning additional offset times. Furthermore, in the proposed scheme, unicast bursts avoid contention with deflection routing. Through simulation experiments, we show that the proposed scheme improves the loss probabilities of both of unicast bursts and multicast bursts.