  In the next-to-minimal supersymmetric model (NMSSM) a light CP-odd Higgs
boson is so far allowed by current experiments, which, together with a large
tan-beta, may greatly enhance the rare dileptonic decays B-> X_s l^+ l^- and
B_s-> l^+ l^- gamma. We examine these decays paying special attention to the
new operator allowed by the light CP-odd Higgs boson. We find that in the
parameter space allowed by current experiments like LEP II and b-> s gamma, the
branching ratios of these rare decays can be greatly enhanced and thus the
existing experimental data on B-> X_s mu^+ mu^- can further stringently
constrain the parameter space (especially the region with a super-light CP-odd
Higgs boson and large tan-beta). In the surviving parameter space we give the
predictions for other dileptonic decay branching ratios and also show the
results for the forward-backward asymmetry.
