An approach called hybrid evidential reasoning is proposed based on the extension principle to deal with multiple attribute decision making under uncertainty. Heterogeneous beliefs, such as crisp value, interval value and fuzzy value, on the same problem are all decomposed into interval value to setup a uniform belief structure. Interval evidential reasoning is used to work out the interval utility of the alternative for each membership degrees, and the utility of each alternative can be assembled in the order of membership degrees. The equation of fuzzy centroid is reduced and used to calculate the belief degree of quantitative fuzzy assessment and rank the fuzzy utility of alternatives. Finally, an example is examined to illustrate the effectiveness and feasibility of the proposed method. Comparing with the application of all these approaches to the example, the results show that the proposed approach is adaptable.