The lagged effect is a common phenomenon in the process of supply chain advertising，which plays an important role in making cooperative advertising strategy of supply chains． This paper studies cooperative advertising strategy in a supply chain having lagged effect on the product’s brand goodwill and develops a dy-namic brand goodwill model with time-delay and a product sales model with brand goodwill． By applying the Maximum principle，the optimal advertising strategies of both the manufacturer and the retailer，the brand goodwill of product，and the entire supply chain profit are obtained in the decentralized and centralized deci-sions，respectively． Also，the optimal advertising cost sharing rate is given in the decentralized decision． The results indicate that the optimal advertising investment and the sales of products are higher in the centralized decision than in the decentralized decision，yet the entire supply chain profit is higher in the centralized deci-sion when the delay time is less than a given threshold value． The results also offer a reference for making ad-vertising strategy and choosing decision mechanism in a supply chain． Finally，numerical examples illustrate the impact of delay time on the optimal advertising strategy and decision mechanism．