We build a two-stage stochastic R&D portfolio model for climate policy analysis. This model can help policy makers allocate a limited R&D budget to minimize the total social cost. We develop several methods, including genetic programming and a greedy algorithm, to deal with the computational challenges of the model that arise due to the inclusion of uncertainties. From the R&D model, we have several key results. First, the optimal portfolios are robust against the climate risks. Second, policy makers should put most of their investment into Carbon Capture and Storage (CCS) projects when the R&D budget is relatively low. We further show Fast Reactor (FR) and 3rd generation PV are the two most unattractive technologies in the portfolio. Finally, more sophisticated expert elicitations on climate change energy technologies should be done in the future, because the potential benefit can be up to 11 billion dollars.