A dominance method is proposed to solve mixed-measure decision problems based on the comparison alternative approaches. A group of dominances is defined and certain some dominance formulas are improved. The complementarily and consistency of the dominance matrix are validated. Then, a sorting method is investigated from the perspectives of sorting vector, dominance vector and comparing vector, respectively. A comparison is donducted between the proposed method and linear weighting methods and ideal point methods. Finally, numerical example illustrates that the proposed method has advantages such as low complexity, high precision and good versatility.