In IEEE 802.11p/1609-based vehicular networks, vehicles are allowed to exchange safety and control messages only within time periods, called control channel (CCH) interval, which are scheduled periodically. Currently, the length of the CCH interval is set to the fixed value (i.e. 50ms). However, the fixed-length intervals cannot be effective for dynamically changing traffic load. Hence, some protocols have been recently proposed to support variable-length CCH intervals in order to improve channel utilization. In existing protocols, the CCH interval is subdivided into safety and non-safety intervals, and the length of each interval is dynamically adjusted to accommodate the estimated traffic load. However, they do not consider the presence of hidden nodes. Consequently, messages transmitted in each interval are likely to overlap with simultaneous transmissions (i.e. interference) from hidden nodes. Particularly, life-critical safety messages which are exchanged within the safety interval can be unreliably delivered due to such interference, which deteriorates QoS of safety applications such as cooperative collision warning. In this paper, we therefore propose a new interference-aware Dynamic Safety Interval (DSI) protocol. DSI calculates the number of vehicles sharing the channel with the consideration of hidden nodes. The safety interval is derived based on the measured number of vehicles. From simulation study using the ns-2, we verified that DSI outperforms the existing protocols in terms of various metrics such as broadcast delivery ration, collision probability and safety message delay.