Abstract: This paper presents an interpolation methods for nearly arc length parameterization of parametric curves. The arc length functions of parametric curves are monotonic descreasing, nearly arc length parameterizations can be converted into monotonity preserving interpolations of arc length functions by piecewise rational linear polynomials. With the interpolation, resulting nearly arc length parameterized curve interpolates a set of points of original curve. Two numerical examples illustrate the parameterized curves are also likely to have shapes that are close to those of the original curves with nowanted oscillations.