This　paper　presents　for　the　first　time　the　concept　of　anisotropy　of　measurement　for　complex　curved　surfaces.　Based　on　the　theory　of　differential　geometry,　the　relation　between　measurement　error　and　micro-structure　&　form　of　curved　surfaces　is　studied,　which　is　existence　proof　of　anisotropy,　and　also　the　basic　rule　of　anisotropy　is　clarified.　Through　anisotropic　analysis　of　the　measurement　for　complex　curved　surfaces,　series　of　conclusions　relating　to　that　are　obtained.　Those　conclusions　have　not　only　theoretical　meaning　but　also　far-reaching　practical　value　on　the　following　aspects:　precision　instruments　design,　error　budget,　measuring　method　design,　and　etc..