As an important tool for multi-criteria decision making in database systems, the regret minimization query is shown to have the merits of top-k and skyline queries: it controls the output size while does not need users to provide any preferences. Existing researches verify that the regret ratio can be much decreased when interaction is available. In this paper, we study how to enhance current interactive regret minimization query by sorting mechanism. Instead of selecting the most favorite point from the displayed points for each interaction round, users sort the displayed data points and send the results to the system. By introducing sorting mechanism, for each round of interaction the utility space explored will be shrunk to some extent. Further the candidate points selection for following rounds of interaction will be narrowed to smaller data spaces thus the number of interaction rounds will be reduced. We propose two effective sorting-based algorithms namely Sorting-Simplex and Sorting-Random to find the maximum utility point based on Simplex method and randomly selection strategy respectively. Experiments on synthetic and real datasets verify our Sorting-Simplex and Sorting-Random algorithms outperform current state-of-art ones.