Prior economic analysis of reward system and patent system have little attention to innovation research options and environmental externalities. Unlike those prior analyses, this paper examines reward system and patent system with environmental externality in the context of research with two alternatives: normal innovation and environmental innovation. This paper discribes the following: Under a patent system, the innovator never prefers environmental innovation research to normal innovation research. On the other hand, under the reward system the innovator will prefer to environmental innovation research unless environmental damage's range is sufficient narrow. Furthermore, this paper shows reward system is more desirable than patent system for environmental innovation.