In variable precision rough set, by introducing inclusion degree β, attribute reduction has been diversified. For example, in variable precision rough set, many researchers have studied β-reduct, β lower distribution reduct and β upper distribution reduct and so on. In this paper, we further research on β-reduct. We first discuss the monotonic characteristics of β lower and β upper approximation with the changes of the parameter β . Then we cite an example to illustrate the fact that with the change of the inclusion degree β, there is no monotonic characteristic in β-reduct. Finally, we develop an improved algorithm of finding β-reduct by considering the combinations among the condition equivalence classes.