We point out another important production channel of a light pseudoscalar Higgs boson a1 via the decays of neutralinos, including χ˜2,30→χ˜10a1, in the framework of the NMSSM. We scan the whole parameter space using the most up-to-date version of NMHDECAY and search for regions where B(χ˜2,30→χ˜10a1)>0.5. If the gluino and squarks are light enough for copious production of SUSY events at the LHC, there would be numerous number of χ˜2,30 in subsequent decays of gluinos and squarks. Therefore, the production rates of a1 via neutralino decays would be more important than h→a1a1 and others. Potentially, the final state is filled with many τ leptons, which may be reconstructed at the mass of a1. However, it suffers from large backgrounds and poor efficiencies.