Measuring　and　evaluating　the　geometric　error　of　a　linear　axis　periodically,　is　an　essential　operation　in　the　day-to-day　usage　of　a　machine　tool.　In　this　paper,　a　system　consisting　of　a　novel　one-dimension　probe　and　a　ball　array　is　developed　to　fast　estimate　the　geometric　error　a　linear　axis　from　the　ball　center　deviations　in　three　dimensions.　The　proposed　1D　probe　is　assembled　by　an　inductance　micrometer　and　a　simple　fixture.　Five　measuring　positions　on　the　ball　surface　are　selected　to　recognize　the　ball　center　offset　caused　by　the　geometric　error.　Then,　an　identification　model　is　established　to　recognize　the　error　at　the　ball　center　in　the　array.　Moreover,　a　correction　method　is　proposed　to　eliminate　the　installation　error.　It　applies　the　least　square　method　to　form　the　virtual　baseline　by　the　measured　ball　centers,　in　order　to　eliminate　the　effect　that　resulted　from　the　inaccuracy　and　the　misalignment　of　the　ball　array　during　the　manufacturing　and　setting,　respectively.　Then,　the　remaining　part　of　the　measured　results　is　applied　to　evaluate　the　geometric　error　of　the　measured　linear　axis,　including　one　positioning　error　and　two　straightness　errors.　Finally,　a　prototype　system　is　developed　to　verify　the　correctness　of　the　proposed　1D　probe,　while　a　measurement　experiment　is　conducted　on　a　machining　center　to　verify　the　validity　of　the　proposed　method.　The　results　indicate　that　the　maximum　absolute　error　among　one　positioning　error　and　two　straightness　errors　reach　to　2.1　μm,　2.3　μm,　and　1.6　μm,　respectively,　while　the　root　mean　square　error,　and　the　average　absolute　error　are　no　more　than　2.0　μm,　when　comparing　with　the　results　from　the　laser　interferometer.　©　2021,　The　Author(s),　under　exclusive　licence　to　Springer-Verlag　London　Ltd.,　part　of　Springer　Nature.