Purpose　This　study　aims　to　satisfy　the　thermal　management　of　gallium　nitride　(GaN)　high-electron　mobility　transistor　(HEMT)　devices,　microchannel-cooling　is　designed　and　optimized　in　this　work.　Design/methodology/approach　A　numerical　simulation　is　performed　to　analyze　the　thermal　and　flow　characteristics　of　microchannels　in　combination　with　computational　fluid　dynamics　(CFD)　and　multi-objective　evolutionary　algorithm　(MOEA)　is　used　to　optimize　the　microchannels　parameters.　The　design　variables　include　width　and　number　of　microchannels,　and　the　optimization　objectives　are　to　minimize　total　thermal　resistance　and　pressure　drop　under　constant　volumetric　flow　rate.　Findings　In　optimization　process,　a　decrease　in　pressure　drop　contributes　to　increase　of　thermal　resistance　leading　to　high　junction　temperature　and　vice　versa.　And　the　Pareto-optimal　front,　which　is　a　trade-off　curve　between　optimization　objectives,　is　obtained　by　MOEA　method.　Finally,　K-means　clustering　algorithm　is　carried　out　on　Pareto-optimal　front,　and　three　representative　points　are　proposed　to　verify　the　accuracy　of　the　model.　Originality/value　Each　design　variable　on　the　effect　of　two　objectives　and　distribution　of　temperature　is　researched.　The　relationship　between　minimum　thermal　resistance　and　pressure　drop　is　provided　which　can　give　some　fundamental　direction　for　microchannels　design　in　GaN　HEMT　devices　cooling.