This paper using endogenous growth models based on research and development, has investigated two economic relations in three groups of countries included developed countries, developing countries and a mixed group of both mentioned ones. At first, the effects of R&D activities on patent growth have examined and then the relation between volume of patent and growth rate in these groups has surveyed. One of the problems for estimating endogenous growth model based on R&D is finding a suitable representative for qualitative variables, we use gross R&D expenditures as a criterion for measurement of endogenous investment for changing the technology. Useful patent is a proxy for growth rate of patent result in investment in R&D field. In addition, growth of total factor productivity is the proxy for changing in technology and the growth rate of GDP as a criterion for economic growth has taken place. Results of this paper show that investment in R&D activities has significant and positive effect on patent flow in both developed and developing countries and also this effect is greater in developing countries than developed countries. Moreover in developing countries, effect of growth in R&D expenditure on growth of patent flow is 6 times of developed countries. The other finding is that in developing countries, effect of increasing patent on additional GDP is greater than the corresponding factors in developed countries. And finally, investment in R&D activities has significant and positive effect on growth of gross national output in both groups of countries.