Using the first-principles calculational method based on the density functional theory, we study the structural instabilities, phonon softenings, and their relation to the superconductivities of two -pyrochlore oxide superconductors AOs2O6(A=K, Rb). It is found that there are structural instabilities of alkali ions along the 〈111〉 direction in the two -pyrochlore oxide superconductors AOs2O6(A=K, Rb), especially in KOs2O6. Meanwhile, a comparison of the phonon frequency at zone-center between KOs2O6 and RbOs2O6 shows that the frequency of KOs2O6 is lower in general than that of RbOs2O6, leading to the stronger electron-phonon coupling. We conclude that K atom located in a large oxygen cage has an unusual large atomic displacement parameter and strong activity, thereby resulting in strong phonon softening. This is the foundamental cause for stronger electron-phonon coupling and higher superconducting transition temperature of KOs2O6. These are of significance for explaining the superconductivities in -pyrochlore oxide superconductors AOs2O6(A=K, Rb).