Valuation of infrastructure systems under climate change is a challenging issue because climate changes constantly and the influence of climate change is hardly predictable. Serious climate change effects can often be represented by frequent heavy rainfall events and floods. In response, municipalities should improve existing drainage systems to adapt to climate change. However, it is difficult to properly determine when or how to improve these systems because different investment strategies could result in entirely different outcomes. This study proposes a decision framework that can assist municipalities in identifying an optimal infrastructure investment strategy under climate change using a real option approach. The framework considers the uncertainties of climate change based on the volatility of flood damage and estimates the value of wait option for the improvement investment using binomial model. A case study is conducted to verify the proposed framework and assess how different investment strategies affect the value of a drainage system. The results showed that the system improvement with 100 year-flood design in 2019 was the most beneficial among available alternatives.