Firstly　the　period　averaging　dynamic　model　of　Three-phase　Four-leg　APF　is　established　based　on　KVL.　In　the　light　of　complex　control　and　difficult　implementation　of　dynamic　compensation,　the　nonlinear　mathematical　model　is　changed　into　the　standard　linear　model　by　reasonable　hypothesis.　Secondly　,aiming　at　the　problem　that　the　APF　controller　with　parameters　perturbation　has　low　robust,　with　the　help　of　LMI,　the　improved　non-fragile　H∞　control　on　three-phase　four-leg　APF　is　studied　in　this　paper.Finally,the　simulation　results　are　presented　to　prove　that　the　good　compensation　effect　can　obtained　with　the　parameters　perturbation.　Furthermore　the　closed-loop　APF　can　remain　H∞　index　stable.　©2010　IEEE.