In rough set theory, two crisp sets (i.e., the lower and upper approximates of a target concept) is used to describe uncertainties in given information systems. However, the traditional rough set models are built based on equivalence relations which do not consider the preference relationship of attribute values. Dominance relation-based rough set approach effectively solve this problem which uses dominance relations to substitute equivalence relations to deal with ordered data. In this kind of approach, the computing of dominance class is a necessary step to attribute reduction which is very time-consuming. In order to reduce the computational cost in calculating dominance classes, this paper presents a method to compute dominance classes by gradually reducing the search space in the domain. The corresponding algorithm is proposed. In each step of the algorithm, the inferior classes of the objects in a given information system are removed in the universe with the increase of the attributes. Experiments using six UCI data show that the proposed method improves the efficiency of computing dominance classes with the increasing of attributes and objects.