Scanning worm increases network traffic load and result in severe network congestion because it is a self-replicating worm and send copies of itself to a number of hosts through the Internet. So an early detection system which can automatically detect scanning worms is needed to protect network from those attacks. Although many studies are conducted to detect scanning worms, most of them are focusing on the method using packet header information. The method using packet header information has long detection delay since it must examine the header information of all packets entering or leaving the network. Therefore we propose an algorithm to detect scanning worms using network traffic characteristics such as variance of traffic volume, differentiated traffic volume, mean of differentiated traffic volume, and product of mean traffic volume and mean of differentiated traffic volume. We verified the proposed algorithm by analyzing the normal traffic captured in the real network and the worm traffic generated by simulator. The proposed algorithm can detect CodeRed and Slammer which are not detected by existing algorithm. In addition, all worms were detected in early stage: Slammer was detected in 4 seconds and CodeRed and Witty were detected in 11 seconds.