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.