  Simpson, in 1994, introduced the notion of $\Lambda$-modules and constructed
the corresponding moduli space, where $\Lambda$ is a sheaf of rings of
differential operators. Higgs bundles, connections and $\lambda$-connections
(as defined by Delgine) are particular cases of $\Lambda$-modules. In this
article the concept of parabolic $\Lambda$-modules over a curve is introduced
and their moduli space is built. As an application, we construct the parabolic
Hodge moduli space parameterizing parabolic $\lambda$-connections.
