To　reduce　the　theoretical　measurement　error　caused　by　a　high　acceleration　in　fast　ultra-precision　laser　heterodyne　interferometry,　a　model　is　proposed.　This　model　is　about　how　the　displacement　measurement　precision　is　affected　by　the　acceleration　of　the　measuring　prism　in　a　multi-pass　heterodyne　interferometer.　In　the　model,　the　integrals　of　Nv2/c　and　Nax/c　are　added　on　the　basis　of　a　conventional　heterodyne　interferometer　model.　It　shows,　that　in　the　conventional　model　the　measurement　error　increases　with　increasing　measurement　acceleration.　An　error　compensation　method　is　proposed,　which　uses　numerical　integration　to　obtain　the　real　time　speed　and　acceleration.　Corrected　data　can　be　acquired　by　using　an　error　correction　formula.　Simulation　results　show,　that　the　measurement　error　can　be　reduced　by　this　method　from　10nm　to　0.03nm　when　the　displacement　of　the　measuring　prism　is　500mm　and　the　uniform　acceleration　of　the　measuring　prism　of　a　double　pass　interferometer　equals　g.　©　2008　SPIE.