The anomalies of the moment of inertia in ^170-180Os are analysed in the interacting-boson-plus-fermion-pair model. The angular momentum-angular momentum interaction term (L.L) in the boson Hamiltonian is renormalized by a (1+fL.L)^-1 factor. It was found that the renormalization facilitates the interaction parameter searching and all boson-boson and boson-fermion interaction parameters for the isotope chain can be unified. Energy levels can be reproduced quite well. The general features in the moment of inertia anomalies can be reproduced. The transition quadrupole moments are calculated and compared with other estimates.