This paper formulates a differential game model by extending the classical Lanchester model which involves two duopolistic firms competing for market share through goodwill accumulation and quality improvement activities, and investigates the optimal advertising and quality improvement strategies for the two duopolistic firms in which the goodwill is devoted to attracting new customers. By using the numerical analysis methods to define the optimal control path for advertising and quality improvement efforts for the duopolistic firms, the paper obtains some beneficial conclusions for company practice.