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In response to the impacts of extreme precipitation on human or natural systems under climate change, the development of climate risk assessment approach is a crucial task. In this paper, a novel risk assessing approach based on a climate risk assessment framework with copula-based approaches is proposed. Firstly, extreme precipitation indices (EPIs) and their marginal distributions are estimated for historical and future periods. Next, the joint probability distributions of extreme precipitation are constructed by copula methods and tested by goodness-of-fit indices. The future joint probabilities and joint return periods (JRPs) of the EPIs are then evaluated. Finally, change rates of JRPs for future periods are estimated to assess climate risk with the quantitative data of exposure and vulnerability of a protected target. An actual application in Taiwan Island is successfully conducted for climate risk assessment with the impacts of extreme precipitation. The results indicate that most of regions in Taiwan Island might have higher potential climate risk under different scenarios in the future. The future joint probabilities of precipitation extremes might cause the high risk of landslide and flood disasters in the mountainous area, and of inundation in the plain area. In sum, the proposed climate risk assessing approach is expected to be useful for assisting decision makers to draft adaptation strategies and face high risk of the possible occurrence of natural disasters.