Consumer privacy information is used to target persuasive advertising in E-commerce, which raises consumer privacy concern. Consumer privacy concern is relative to consumer's intrinsic privacy concern and social concern over the application of consumer privacy information, known as the anchoring effect of privacy. The anchoring effect of privacy influences targeted persuasive advertising competition. With a game-theoretical model, this paper studies how asymmetric duopolistic firms compete with targeted persuasive advertising considering the anchoring effect of privacy. The results indicate that when the advantageous firm increases its advertising level, the advantageous firm gets more profit, and the disadvantageous firm gets less profit only if the anchoring effect of privacy is greater than zero. Otherwise, the disadvantageous firm gets more profit, but the advantageous firm gets less profit. Then, in equilibrium, the increase in the expected anchoring effect of privacy, expected consumer's intrinsic privacy concern, and advertising influence power reinforce the competition asymmetry. Whereas, the increase in social concern over the application of consumer privacy information weakens the competition asymmetry. Purpose: This paper aims to analyze the competitive targeted persuasive advertising strategy considering the anchoring effect of privacy, which is relative with consumer intrinsic privacy concern and social concern. Methods: A three-stage theoretical model is established to study the targeted persuasive advertising strategy. In the model, two competitive firms compete with targeted persuasive advertising and price, and the anchoring effect of privacy, advertising persuasive power and product prices influence consumers' purchase decisions. Conclusions: We find that when the advantageous firm increases its advertising level, only if the anchoring effect of privacy is greater than zero, the advantageous firm gets more profit, and the disadvantageous firm gets less profit. Moreover, the increase in the expected anchoring effect of privacy, expected consumer's intrinsic privacy concern, and advertising influence power reinforce the competition asymmetry. Whereas, the increase in social concern over the application of consumer privacy information weakens the competition asymmetry. Implications: We suggest that firms should be cautious about increasing their advertising levels in competition, because they may suffer the loss with a greater advertising level due to the existence of the anchoring effect of privacy. Then, when competing with targeted persuasive advertising and price, the firm with low quality-cost margin should try to eliminate the asymmetry between itself and its competitor. Limitations: Firstly, the model in this paper does not cover all the features of the competition markets. Secondly, we just assume that persuasive advertising enhances consumer's perceived quality, where persuasive advertising may alter consumer preference. Thirdly, it is interesting to investigate and verify our research topic with empirical approach.