The　quasi-rigid　body　model　is　the　relationship　model　between　the　volume　error　and　the　geometric　error　of　the　CMM　under　the　consideration　of　simple　deformation.　The　quasi-rigid　body　model　reflects　the　comprehensive　influence　of　all　geometric　errors　and　ensures　the　calibration　accuracy　of　geometric　errors.　However,　the　geometric　error　solution　based　on　the　quasi-rigid　body　model　has　the　problem　of　multicollinearity.　To　solve　this　problem,　in　this　study,　the　geometric　errors　of　CMM　are　compensated　using　laser　tracing　multistation　measurement　technology　and　the　LASSO　(Least　absolute　shrinkage　and　selection　operator,　LASSO)　algorithm.　First,　a　laser　tracing　multi-station　measurement　model　is　established,　and　then　the　coordinates　of　the　laser　tracer　station　are　obtained　by　solving　the　redundant　equations　provided　by　the　laser　tracer　multi-station　measurement　system　using　the　L-M　(Levenberg　Marquardt)　algorithm.　The　global　positioning　system　localization　principle　combined　with　the　L-M　algorithm　is　used　to　determine　the　actual　position　of　the　CMM　measurement　point.　Then,　the　volume　error　is　determined　by　calculating　the　difference　between　the　actual　position　of　the　measurement　point　and　the　planned　position.　A　mathematical　model　of　the　volumetric　and　geometric　errors　is　obtained　from　the　CMM　quasi-rigid　body　model,　and　the　LASSO　algorithm　is　used　to　solve　the　model　to　obtain　the　17　geometric　errors　of　the　CMM.　Using　the　relationship　between　the　volume　error　and　the　uniaxial　geometric　error,　the　4　rotational　errors　are　solved　of　epsilon(z)　(x),　epsilon(x)-　(z),　epsilon(v)　(z),　epsilon(z)　(z).　To　verify　the　measurement　accuracy　of　the　compensated　CMM,　the　compensation　effect　is　verified　by　using　the　XL80　interferometer　with　the　measuring　block.　The　experimental　results　indicate　that　when　error　compensation　is　performed,　the　measurement　accuracy　of　the　CMM　is　improved　by　＞　50%　compared　to　the　initial　state,　and　no　mechanical　processing　is　involved.