Summary: Let \(H\) be a finite type Hopf \(\pi\)-algebra, the author studies the dual relation between a Hopf \(\pi\)-module of Hopf \(\pi\)-algebra \(H\) and a Hopf \(\pi\)-comodule of Hopf \(\pi\)-coalgebra \(H^*\). Finally, some necessary and sufficient conditions between Hopf \(\pi\)-submodule and Hopf \(\pi\)-subcomodule are obtained.