This paper proposes a fair bandwidth allocation mechanism FPIP(fair PIP). Dealing differently with the packets of long flows and short flows at routers,the mechanism can preferentially allocate the bandwidth of the router to short flows and allocate the remaining among the competing long flows. Furthermore,it can keep the queue length of the router at a reference value using a well-designed active queue management AQM(active queue management) algorithm. The simulation results show that this new mechanism can outperform CSFQ(core-stateless fair queueing) in terms of fairness,queue length and the response time of Web flows.