Distance　measure　is　quite　important　for　pattern　recognition.　Utilizing　invariance　in　image　data,　tangent　distance　is　very　powerful　in　classifying　handwritten　digits.　For　this　measure　a　set　of　invariant　transformations　must　be　known　a　priori.　But　in　many　practical　problems,　it　is　very　difficult　to　know　these　transformations.　In　this　paper,　an　algorithm　is　proposed　to　approximate　the　invariant　tangent　distance　exclusively　from　the　data.　By　virtue　of　ideas　arising　from　manifold　learning,　the　algorithm　needs　no　prior　transformations　and　can　be　applied　to　more　classification　problems.　k-nearest　neighbor　rule　based　on　the　new　distance　are　implemented　for　classification　problems.　Experimental　results　on　synthetic　and　real　datasets　illustrate　its　validity.