Abstract: In order to gain the best R&D competitive strategy of competitive corporations, the amount of investment in R&D, the instantaneous coordination of production and the game process of competition are analyzed, with the factors of the technology spillovers and absorptive capacity considered. By expanding the traditional AJ models to dynamic differential game models, rich dynamic connotation implies that the new model is beneficial to exploring the competing mechanism of duopoly R&D. Based on the methodology of differential games, combined with Pontryagin maximum principle used in optimal control theory, sufficiency and necessity for the equilibrium solution are given; simultaneously, by a numerical simulation analysis of equilibrium solution, the R&D competition strategy is found to be affected by technology spillover and absorptive capacity. This research provides options for achieving path for competing companies to achieve their own maximum benefit or cost minimization by choosing different R&D competing strategies.