In this study, we construct the optimal R&D investment decision-making model under uncertainty by using real options approach and extreme value theory. Then, we use the numerical analysis and sensitivity analysis to explore the influence of relevant parameters on the threshold of the optimal R&D investment decisions. The results showed that: 1. The optimal entry time of R&D investment will delay, by considering the impact of the extreme value distribution under uncertainty. 2. The fuzzy investment decision thresholds of decision model of different extreme value distribution, the Gumbel extreme value distribution is highest, the Fréchet extreme value distribution is second, the Weibull extreme value distribution is lowest. 3. The degree of uncertainty, instantaneous growth rate, investment costs, the scale parameter has the positive relation with the decision thresholds. Risk-free rate, positional parameters and shape parameters has the negative relation with the decision thresholds. 4. Our research model can apply to actual case data, the case study of the Genovate biotech company may elaborate appropriateness of the theoretical model.