In this work, the effect of a special type of neutron-proton pairing interaction on the moments of inertia of some deformed nuclei in the rare earth region is investigated. First, making a perturbative approximation, we assume that the form of the equations of the BCS theory and usual Bogolyubov transformations are unchanged. Second, we use a phenomenological method for the strength of this neutron-proton pairing interaction introducing a parameter. Calculations show that this interaction is important for the ground-state moments of inertia and that it could be effectual in other nuclear phenomena.