This paper extends the product cycles model of Grossman and Helpman(1991a) to explore the dynamics of different FDIs on welfares of the southern country during their economic development process within the North-South framework. We distinguish two types of FDIs, one-way FDI that there is only investment from the North, the developed country to the South, the developing country and two-way FDI that adds the investment from the South to establish R&D centers in the North. We find that the welfare level is keeping decreasing from the situation of no-FDI like the original setting of Grossman and Helpman (1991a) to that of one-way FDI and to that of two-way FDI. Moreover, Our model also yields very rich results concerning the regime effect, the effect of changing the relative size of the North to the South on innovation and imitation, and the effects of innovation policies.