The prosperity of mobile networks and social networks brings revolutionary conveniences to our daily lives. However, due to the complexity and fragility of the network environment, network attacks are becoming more and more serious. Characterization of network traffic is commonly used to model and detect network anomalies and finally to raise the cybersecurity awareness capability of network administrators. As a tool to characterize system running status, entropy-based time-series complexity measurement methods such as Multiscale Entropy (MSE), Composite Multiscale Entropy (CMSE), and Fuzzy Approximate Entropy (FuzzyEn) have been widely used in anomaly detection. However, the existing methods calculate the distance between vectors solely using the two most different elements of the two vectors. Furthermore, the similarity of vectors is calculated using the Heaviside function, which has a problem of bouncing between 0 and 1. The Euclidean Distance-Based Multiscale Fuzzy Entropy (EDM-Fuzzy) algorithm was proposed to avoid the two disadvantages and to measure entropy values of system signals more precisely, accurately, and stably. In this paper, the EDM-Fuzzy is applied to analyze the characteristics of abnormal network traffic such as botnet network traffic and Distributed Denial of Service (DDoS) attack traffic. The experimental analysis shows that the EDM-Fuzzy entropy technology is able to characterize the differences between normal traffic and abnormal traffic. The EDM-Fuzzy entropy characteristics of ARP traffic discovered in this paper can be used to detect various types of network traffic anomalies including botnet and DDoS attacks.