In this paper, we briefly review the LHC discovery potential of a light pseudoscalar Higgs boson of the NMSSM, a1, produced in the gluon fusion gg→a1 , bottom-quark fusion bb¯→a1 and bottom-gluon fusion bg→ba1. We also review the LHC discovery potential of the next-to-lightest CP-even Higgs boson h2 being the non-SM-like Higgs, decaying either into two light CP-odd Higgs bosons a1 or into a light a1 and the Z gauge boson through the gluon fusion gg→h2 in the 4τ final state. We find that the light a1 can be detected at the LHC in a variety of production processes including the gluon fusion, bottom-quark fusion and bottom-gluon fusion. The latter two processes require high luminosity of the LHC and large values of tanβ. We also find that the LHC has the potential to discover the non-SM-like Higgs state, h2, decaying into a pair of light CP-odd Higgses a1’s, allowing the distinguishing of the NMSSM Higgs sector from the MSSM one as such a light a1, is impossible in the latter scenario.