We present a parametric groundness analysis whose input and output are parameterized by a set of groundness parameters. The result of the analysis can be instantiated for different uses of the program. It can also be used to derive sufficient conditions for safely removing groundness checks for built-in calls in the program. The parametric groundness analysis is obtained by generalizing a non-parametric groundness analysis that uses the abstract domain Con. It is shown to be as precise as the non-parametric groundness analysis for any possible values for the groundness parameters. Experimental results of a prototype implementation of the parametric groundness analysis are given.