Scanning worms increase network traffic load because they randomly scan network addresses to find hosts that are susceptible to infection. Since propagation speed is faster than human reaction, scanning worms cause severe network congestion. So we need to build an early detection system which can automatically detect and quarantine such attacks. We propose algorithms to detect scanning worms using network traffic characteristics such as variance, variance to mean ratio(VMR) and correlation coefficient. The proposed algorithm have been verified by computer simulation. Compared to existing algorithm, the proposed algorithm not only reduced computational complexity but also improved detection accuracy.