A　complex　Computed　Numerical　Control　(CNC)　grinding　precision　machining　equation　was　established　to　improve　the　machining　precision　of　the　composite　CNC　grinding　machine.　A　software　for　the　corresponding　compensation　was　developed,　and　the　precision　modeling,　error　identification,　error　compensation,　etc.　for　the　complex　CNC　grinding　machine　were　researched.　Firstly,　the　multi-body　system　modeling　theory　was　used　to　analyze　the　CNC　thread　grinder　modeling.　The　precision　machining　equation　of　CNC　grinding　machine　was　established.　Then　all　the　composite　errors　of　CNC　grinding　machine　were　identified　by　using　a　laser　interferometer.　Finally,　the　error　before　and　after　error　compensation　were　forecasted　and　the　feasibility　of　the　theory　for　geometric　error　compensation　was　finally　verified.　The　simulation　results　show　that　errors　have　been　decreased　by　66.55%,　66.65%　and　66.35%　in　X　axis,　Z　axis　and　C　axis,　respectively,　and　the　integrated　error　for　three　axis　has　reduced　by　66.51%.　It　concludes　that　the　error　compensation　technology　can　be　used　in　thread　processing　fields　and　can　improve　the　machining　accuracy　of　the　CNC　grinding　machines.　©　2015,　Chinese　Academy　of　Sciences.　All　right　reserved.