Argumentation is a kind of interaction between agents for resolving differences in speech. Due to the limitation of knowledge, arguments and its inner statements are usually uncertain, and therefore it is necessary to consider uncertain information processing when modeling the process of argumentation. This paper proposes an argumentation model based on the theory of certainty-factor, in which an argument is expressed as a defeasible rule with several premises but only one conclusion, and the process of argumentation is described as a dialogue tree. In order to do uncertain reasoning, the uncertainty of argument's premise and the strength of the attack that one argument makes against another are assigned with certainty-factors. Next, the algorithms of argument evaluation are provided to compute the credibility of statements. Using the algorithms the set of acceptable arguments can be determined by the credibility threshold and the result of argumentation can be obtained. Finally, an example is given to illustrate the validity of the method. The algorithms are based on numerical computation where the set of acceptable arguments is unique under a given credibility threshold, and can overcome the shortage of extension semantics of Dung's abstract argumentation framework.