Abstract: For a class of evidence fusion problems that integrate different importance with credibility, a new weighted average method based on overall weight of discounted evidence is proposed by combining the static weight with the dynamic weight embodying the similarity between evidences. According to the transcendental information, i.e., static weight and the similarity between evidences, the dynamic weight of evidence is acquired by calculating the distances between all evidences discounted via a static weight computation and their weighted average, then the static weight is integrated with dynamic weight to form an overall weight of evidence. An evidential reasoning model is thus developed with some discount, where the overall weight plays the role as a discounting factor. Finally, the modified evidences are combined together by the weighted average method proposed. A numerical example shows the effectiveness of the method in the integration of those evidences which are in sharp conflict with each other.