Abstract: The error estimation of rational cubic spline with linear denominators is given,and then the interpolation of a kind of space closed curves under cylindrical coordinate system is investigated.The main idea is to transform the interpolation problem of space closed curves into the one of plane curves by rational cubic splines with linear denominators through expanding circular cylindrical surface.The space curves finally obtained are shown to be curvature continuous.The error estimation of this method is also analyzed,and numerical examples show that the effect of interpolation is improved.