  We analyse the CP asymmetry of the B -> phi K_S and B -> eta' K_S processes
in general supersymmetric models. We show that chromomagnetic type of operator
may play an important role in accounting for the deviation of the mixing CP
asymmetry between B -> phi K_S and B -> J/psi K_S processes observed by Belle
and BABAR experiments. We also show that due to the different parity in the
final states of these processes, their supersymmetric contributions from the
R-sector have an opposite sign, which naturally explain the large deviation
between their asymmetries.
