The purpose of this research is to design a new queue management algorithm effectively controlling the heavy-tailed traffics. Among active queue managements (AQM), random early detection (RED), has been widely used to improve the TCP throughput. The heavy-tailed traffic, however, generates the large fluctuation on the queue causing the degradation of fairness in terms of throughput and jitter performance. In this paper, we proposed the stable time RED (ST-RED) to improve the fairness of throughput and jitter performance. ST-RED enables to stabilise the calculation timing for average queue length leading to suppress the queue fluctuations. We also implemented the ST-RED mechanism on the ns-2 simulator. As results of simulation, we extracted the following features. Firstly, RED improves the throughput and reduces the overall load balance leading to the improvement of its fairness with all different alpha s of the Pareto distribution. Secondly, ST-RED keeps the same TCP throughput performance for each traffic with different alpha of the Pareto distribution as RED does. Thirdly, ST-RED with 0.5 msec time interval slightly improves the throughput fairness for all traffics. In addition, our proposed method clearly improves the fairness of jitter on a large scale compared to the original RED.