A　series　of　polymeric　ionic　liquids　(PILs)　used　as　effective　heterogeneous　catalysts　for　biodiesel　production　via　esterification　of　free　fatty　acids　(FFAs)　were　effectively　prepared　by　the　reaction　of　poly　(ethylene　imine)　(PEI)　polymers　with　different　molecular　weight　and　1,3-propanesultone,　followed　by　the　further　acidification　with　differential　effective　acids,　i.e.　H2SO4,　CF3SO3H,　CH3SO3H　or　p-toluenesulfonic　acid　(p-TSA).　Ultrahigh　acidity　and　catalytic　performance　were　achieved　and　could　be　fine-tuned　by　simply　adjusting　the　molecular　weight　of　PEI　and　by　further　treatment　of　acids.　Specifically,　under　the　optimal　conditions　(i.e.　reaction　temperature　was　70　°C,　reaction　time　was　2.0　h,　catalyst　dosage　was　3.15%　(mass),　and　alcohol/acid　molar　ratio　was　14:1)　acquired　through　the　Box-BEHNKEN　response　surface　methodology,　a　high　oleic　acid　conversion　of　98.42%　could　be　obtained　over　the　optimal　PIL,　PEI(70000)-PS-p-TSA.　Additionally,　our　PILs　also　showed　high　generality　for　esterification　of　other　FFAs,　with　general　high　conversion　over　90%　noted　in　each　case　even　under　much　milder　reaction　conditions　compared　to　other　conventional　catalysts.　©　2021　The　Chemical　Industry　and　Engineering　Society　of　China,　and　Chemical　Industry　Press　Co.,　Ltd