In　this　study,　a　stochastic　user　equilibrium　model　on　the　modified　random　regret　minimization　is　proposed　by　incorporating　the　asymmetric　preference　for　gains　and　losses　to　describe　its　effects　on　the　regret　degree　of　travelers.　Travelers　are　considered　to　be　capable　of　perceiving　the　gains　and　losses　of　attributes　separately　when　comparing　between　the　alternatives.　Compared　to　the　stochastic　user　equilibrium　model　on　the　random　regret　minimization　model,　the　potential　difference　of　emotion　experienced　induced　by　the　loss　and　gain　in　the　equal　size　is　jointly　caused　by　the　taste　parameter　and　loss　aversion　of　travelers　in　the　proposed　model.　And　travelers　always　tend　to　use　the　routes　with　the　minimum　perceived　regret　in　the　travel　decision　processes.　In　addition,　the　variational　inequality　problem　of　the　stochastic　user　equilibrium　model　on　the　modified　random　regret　minimization　model　is　given,　and　the　characteristics　of　its　solution　are　discussed.　A　route-based　solution　algorithm　is　used　to　resolve　the　problem.　Numerical　results　given　by　a　three-route　network　show　that　the　loss　aversion　produces　a　great　impact　on　travelers＇　choice　decisions　and　the　model　can　more　flexibly　capture　the　choice　behavior　than　the　existing　models.