  We construct here the parametric representation of a translation-invariant
renormalizable scalar model on the noncommutative Moyal space of even dimension
$D$. This representation of the Feynman amplitudes is based on some integral
form of the noncommutative propagator. All types of graphs (planar and
non-planar) are analyzed. The r\^ole played by noncommutativity is explicitly
shown. This parametric representation established allows to calculate the power
counting of the model. Furthermore, the space dimension $D$ is just a parameter
in the formulas obtained. This paves the road for the dimensional
regularization of this noncommutative model.
