Dissociation dynamics of a size-selected sodium cluster ion, Na-9(+), in collision with a series of rare-gas atoms, He, Ne, Ar, Kr and Xe, was investigated by measuring the absolute cross sections by use of a tandem mass-spectrometer, The dominant processes for the dissociation are Na and Na-2 release from the parent cluster ion. Total cross sections for the dissociation except for the Xe collision is explained in a scheme of classical collision. In the Xe collision, it was found that the cross sections observed were smaller than the cross sections predicted by the classical collision scheme, probably because of long range interaction between the cluster ion and Xe atom. On the other hand, the branching fractions for the Na and the Na-2 release are predicted well by the orbital correlation diagrams for the dissociation systems.