The　3-ary　n-cube,　denoted　as　Qn3,　is　an　important　interconnection　network　topology　proposed　for　parallel　computers,　owing　to　its　many　desirable　properties　such　as　regular　and　symmetrical　structure,　and　strong　scalability,　among　others.　In　this　paper,　we　first　obtain　an　exact　formula　for　the　minimum　wirelength　to　embed　Qn3　into　grids.　We　then　propose　a　load　balancing　algorithm　for　embedding　Qn3　into　a　square　grid　with　minimum　dilation　and　congestion.　Finally,　we　derive　an　O(N2)　algorithm　for　embedding　Qn3　into　a　gird　with　balanced　communication,　where　N　is　the　number　of　nodes　in　Qn3.　Simulation　experiments　are　performed　to　verify　the　total　wirelength　and　evaluate　the　network　cost　of　our　proposed　embedding　algorithm.　©　2019,　Springer　Science+Business　Media,　LLC　&　Science　Press,　China.