The theory and methods of feature selection of the covering decision information system, whose decision is characterized by partition, are becoming mature. However, the decision attribute values of some objects in some data sets are missing or fuzzy. Then, it is reasonable to characterize the decision as a covering, but the study on feature selection of covering decision information system whose decision is characterized by covering is still very rare. In this paper, we discuss feature selection of covering decision information system whose decision is characterized by covering. We present a definition of attribute reduction in covering decision information system, and employ belief and plausibility functions from evidence theory to characterize the attribute reductions in covering decision information systems. Then, an attribute reduction algorithm based on evidence theory is proposed in covering decision information systems, and an example is used to illustrate the validity of the method.