Abstract: By analogizing microblog users to nodes and the followingship of a user to others to directed edges in a network graph, PageRank algorithm can be used to compute the influence of a microblog user. However the unrevised PageRank is based on the condition that the weights of directed edges of a node pointing to others are equal. Obviously this condition is not applicable to compute the influence of microblog users. Because of the existence of natural differences among interests, ideologies, posting frequencies of users, someone must follow different users she or he following to different extend. By computing the interest similarity, relative posting frequency, feedback frequency of a user to another to measure the following degrees of the user to her or his followings, this article develops a new algorithm, WeiboRank, which is based on PageRank to compute the influence of a user on a microblog platform. The experiment result shows that the influence value of a user computed by using WeiboRank can reflect the actual influence of the user in an on-line social circle in which she or he is.