In this paper, the time complexity of the HEWN algorithm for the maximum clique problem is analyzed. Firstly, a sort of data structure to implement the HEWN algorithm is designed by analyzing the structural characters of HEWN and the needed operations. It is pointed out that the storage structure of HEWN should use the linked list which combine adjacency multi-list with binary linked list. And then, the building procedure of HEWN is anatomized by starting with the storage structure of HEWN. In the anatomizing procedure, by comparing with the MCST, it is pointed out that underlying exponential times of creating and modifying GM exists in the HEWN algorithm when 2j>n. Therefore, the time complexity of the HEWN algorithm is exponential instead of O(n^8.5).