Intertemporal choice refers to a choice between alternatives that differ in size and time to delivery. In view of the fact that situations are uncertain in most real-world decisions,a general theoretical model of intertemporal choice must deal with situations involving risk. Beyond the weakness of the previous theoretical models,we will use both the lab method and paper-pencil test to investigate the impact of the probability level on intertemporal choices. Furthermore,the query technique will allow us to explore its process mechanism and test several explanation models（e.g.,the equivalent replacement model） . In order to assess the practical implication of the intertemporal choice under risk in the real world,we will also try to investigate the intertemporal choice as a function of some economic index（e.g.,Consumer Price Index）.