Recently, adaptive interpolation filter (AIF) has received increasing attention for motion-compensated prediction (MCP). The existing methods code the filter coefficients individually and the accuracy of coefficients and the size of side information are conflicting. This paper studies the effect of making trade-off between the two conflicting aspects and proposes the parametric interpolation filter (PIF), which represents filters by five parameters instead of individual coefficients and approximats the optimal filter by tuning the parameters. The experimental results show that PIF approaches the efficiency of the optimal filter and outperforms the related work.