In　ultra-precision　fly-cutting　machining,　the　aerostatic　spindle　is　the　key　component,　which　has　significant　influence　on　the　machined　surface　quality.　The　unbalanced　spindle　directly　affects　the　machining　accuracy.　In　this　article,　a　prediction　model　of　machining　surface　topography　is　proposed　which　involves　the　effect　of　the　gas　film　performance　of　spindle　in　microscale.　With　the　Weierstrass　function,　unstable　transient　response　of　the　aerostatic　spindle　system　is　derived　by　the　motion　model　of　the　spindle,　which　response　signal　represents　the　surface　profile　in　the　ultra-precision　machining.　Meanwhile,　the　experiment　is　performed　with　different　rotation　speed　of　the　spindle.　And　the　effect　of　the　unbalanced　aerostatic　spindle　on　the　surface　generation　is　discussed　in　time　and　frequency　domain.　The　conclusion　shows　that　the　similar　cyclical　surface　ripple　of　the　workpiece　is　independent　of　the　spindle　speed,　and　the　rotation　speed　of　the　spindle　and　unbalanced　spindle　directly　affects　the　machining　surface　topography.　This　study　is　quite　meaningful　for　deeply　understanding　the　influence　rule　of　spindle　unbalanced　error　from　the　viewpoint　of　machined　surface　and　vibration　frequency.