An　alternating　direction　Galerkin　method　combined　with　characteristic　technique,　is　established　for　simulation　of　saturated　-　unsaturated　solute　transport　in　porous　media　in　order　to　overcome　numerical　diffusion　and　oscillation　and　ensure　high　accuracy　and　efficiency　of　computation.　A　novel　characteristic　method,　based　on　single　particle　tracking　of　front　and　high　order　and　linear　interpolations　near　the　front　and　the　remaining　parts　of　domain　respectively　to　obtain　the　＇convective　contribution＇,　is　also　developed.　For　examination　of　the　model,　an　idealized　contaminant　pollution　of　aquifer　and　an　experiment　of　wastewater　disposal　are　simulated.　-Author