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.