For a given set of data elements, the importance estimation is an important application in data mining. The existing work identifies important entities either by ranking or by selection. The major shortcoming of such approaches is that they ignore the redundancy between high-ranked entities, which may in fact be very similar or even identical. Therefore, in scenarios where diversity is desirable, such methods perform poorly. In this paper, by the combination of the sort and selection, we propose an importance of elements estimation algorithm based on the set cover, Instead of looking at a single set-cover solution, our algorithm computes the importance of entities by counting of the number of good set covers an entity participates. In a user study and an experimental evaluation on real data, we demonstrate that our framework is efficient and provides useful and intuitive results.