Epidemic cyber incidents are caused by malicious websites using exploit kits. The exploit kit facilitate attackers to perform the drive-by download (DBD) attack. However, it is reported that malicious websites using an exploit kit have similarity in their website structure (WS)trees. Hence, malicious website identification techniques leveraging WStrees have been studied, where the WS-trees can be estimated from HTTP traffic data. Nevertheless, the defensive component of the exploit kit prevents us from capturing the WS-tree perfectly. This paper shows, hence, a new WS-tree construction procedure by using the fact that a DBD attack happens in a certain duration. This paper proposes, moreover, a new malicious website identification technique by clustering the WS-tree of the exploit kits. Experiment results assuming the D3M dataset verify that the proposed technique identifies exploit kits with a reasonable accuracy even when HTTP traffic from the malicious sites are partially lost.