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.　©　2017,　Editorial　Office　of　Control　and　Decision.　All　right　reserved.