Search engine advertising is a popular business model for online advertising and recently a new strategy (i.e. competitive advertising) is emerging. Competitive advertising is helpful for organizations to expand market shares from competitors, which is crucial to sustain competitive advantage. To achieve the goal of competitive advertising, appropriate and fruitful competitive keywords should be provided to advertisers. However, existing keywords suggestion methods usually recommend general business keywords based on co-occurrence analysis. They not only fail to enable competitive advertising, but also limit advertisers to a small number of hot keywords, causing high bidding costs. As a response, this study proposes a competitive keywords suggestion method based on query logs. It uses the indirect associations between keywords and the hidden topic information captured by query logs to recommend competitive keywords. Through the method, massive competitive keywords are mined out to help organizations achieve competitive advertising and simultaneously broaden the choices of keywords for search engine advertising. Experiments are conducted to demonstrate that the proposed method could have a good performance than other methods, proving that it can help organizations well achieve the goal of competitive advertising.