The　strength　of　the　tangential　magnetic　field　(TMF)　near　the　tested　material　surface　is　an　important　scale　for　understanding　the　signal　obtained　from　micro-magnetic　testing.The　measurement　accuracy　of　TMF　directly　affects　the　precision　of　micro-magnetic　testing.A　new　method　is　proposed　to　accurately　measure　the　strength　of　TMF.A　Hall　sensor　array　is　employed　to　simultaneously　measure　the　TMF　at　three　given　positions　and　then　linear　extrapolation　operation　is　applied　to　the　measured　results　to　estimate　the　strength　of　TMF　at　the　material　surface.A　regulator　structure,　whose　sizes　are　optimized　by　finite　element　simulations,　is　placed　in　the　space　between　the　two　legs　of　the　ferrite　core　to　improve　the　distribution　of　TMF.More　precisely,　the　regulator　structure　can　help　to　reduce　the　slope　of　the　strength　of　TMF　along　the　direction　vertical　to　the　material　surface.Consequently,　the　measurement　accuracy　of　TMF　can　be　improved　and　the　effect　of　variation　in　lift-off　distance　on　the　measurement　results　can　be　suppressed.Experimental　tests　are　conducted　in　plate　specimen　of　65Mn　steel.The　obtained　results　show　that　with　the　linear　extrapolation　method　the　sensor　possesses　higher　accuracy　in　measuring　the　magnetic　hysteresis　curve　than　the　cases　of　current-based　estimation　method　and　the　method　using　single　Hall　device.In　addition,　when　the　lift-off　distance　of　the　ferrite　core　from　the　material　surface　is　in　the　range　of　0~0.5mm,　the　measurement　error　to　the　saturated　and　residual　magnetic　induction　intensity　are　less　than　1.13%.　©　2020,　The　Editorial　Board　of　Journal　of　Basic　Science　and　Engineering.　All　right　reserved.