  Using the latest PandaX limits on light dark matter (DM) with light mediator,
we check the implication on the parameter space of the general singlet
extension of MSSM (without $Z_3$ symmetry), which can have a sizable DM
self-interaction to solve the small-scale structure problem. We find that the
PandaX limits can stringently constrain such a paramter space, depending on the
coupling $\lambda$ between the singlet and doublet Higgs fields. For the
singlet extension of MSSM with $Z_3$ symmetry, the so-called NMSSM, we also
demonstrate the PandaX constraints on its parameter space which gives a light
DM with correct relic density but without sufficient self-interaction to solve
the small-scale structure problem. We find that in this NMSSM the GeV dark
matter with a sub-GeV mediator has been stringently constrained.
