A series of polymeric ionic liquids (PILs) used as effective heterogeneous catalysts for biodiesel produc-tion 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 ℃,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 com-pared to other conventional catalysts.