The mitigation of climate change is thought by many to be a significant environmental concern. In order to mitigate the bulk of carbon emissions from the electricity sector, large market penetration of renewable energy technologies is a key research issue. The goal of the paper is to address the timing of public R&D investment for renewable technologies in the Japanese electricity sector. The model is cast as a dynamic bottom-up energy-system model and numerically optimized, minimizing a total system cost subject to an accumulated carbon emission constraint. Autonomous energy-efficiency improvement and two-factor learning curves describe the technological development process for each energy technology. With the two-factor learning curve, the model shows that the cost of electricity of renewable technologies can be reduced by up to 43% in the year 2100 if there is no constraint on public R&D budget. Renewable energy sources requires substantial R&D support in their initial phase of development; however, the investment pattern would switch to a path of reducing the amount after 2050. The budget of R&D investment is strictly limited; thus, an important policy objective is to design a dynamic investment schedule that will induce sustainable innovations for green technologies.