The Core Stateless Fair Queuing (CSFQ) is a distributed approach of Fair Queuing (FQ). The limitations include its inability to estimate fairness during large traffic flows, which are short and bursty (VoIP or video), and also it utilizes the single FIFO queue at the core router. For improving the fairness and efficiency, we propose an Enhanced Core Stateless Fair Queuing (ECSFQ) with multiple queue priority scheduler. Initially priority scheduler is applied to the flows entering the ingress edge router. If it is real time flow i.e., VoIP or video flow, then the packets are given higher priority else lower priority. In core router, for higher priority flows the Multiple Queue Fair Queuing (MQFQ) is applied that allows a flow to utilize multiple queues to transmit the packets. In case of lower priority, the normal max-min fairness criterion of CSFQ is applied to perform probabilistic packet dropping. By simulation results, we show that this technique improves the throughput of real time flows by reducing the packet loss and delay.