A sentiment lexicon is an important foundation for social network sentiment analysis. However, in social networks, the sentiments of words vary with their topics of use, which leads to a problem in the construction of a sentiment lexicon. We propose a method for constructing a topic-specific sentiment lexicon, which comprises three following models: first, we propose a filtering text model, namely, FT model, to calculate the text influence value and obtain topic-specific hot comments as a preprocessing data set; second, in our proposed constructing sentiment relationship graph model, namely, CRM model, three factors, i.e., the base sentiment similarity, topic sentiment similarity, and synonym sentiment similarity between each pair of sentiment words, are proposed and calculated in our data set, and then we can obtain the factor of final sentiment similarity by adding the three values in proportion; and finally, we propose a spectral clustering model, namely, SC model, to cluster the sentiment words on the basis of a sentiment relationship graph for obtaining the topic-specific sentiment lexicon, namely, STCS lexicon. Experiments show that our method is simple, flexible, and efficient. It can solve the problem of topic-related sentiment words and, thus, improve the accuracy of the sentiment lexicon.