The hybrid fiber coax (HFC) technology enables the conventional cable-television (CATV) network to provide subscribers with Internet access services. In this paper, we propose a new preemptive priority scheme (PPS) for IEEE 802.14 hybrid fiber coax (HFC) networks with the intelligent nodes (INs). The INs are placed between the headend controller and stations. By using INs, that stand for downstream subscribers to contend for the demand resources, the collision probability, and the collision resolving period can be reduced. In this paper, we further extend such network architecture to support multi-priority access. In each IN or individual station, the proposed PPS will prevent a higher priority request from colliding with requests of lower priority. Moreover, in PPS, the granted bandwidth for lower priority requests can be preempted by the waiting request with higher priority. This will speedup the channel capture by priority data. The efficiency of PPS is investigated by simulations. Simulation results show that by adopting INs with PPS to be an agent for subscribers can not only shorten the collision resolving period but also minimize the average request delay of priority data.