After the discovery of the Higgs boson with mass around 126 GeV it has to be investigated if it is the Standard Model (SM) Higgs boson or the Higgs boson of extensions beyond the SM (BSM). Among these, supersymmetry (SUSY) belongs to the most popular and most intensely studied BSM theories. The Higgs sector of the Next-to-Minimal Supersymmetric Extension (NMSSM) consists of seven Higgs bosons, two charged Higgs bosons, three neutral CP-even and two CP-odd Higgs bosons. We investigate the discovery prospects of the NMSSM Higgs bosons at the high-energy option of the Large Hadron Collider (LHC). While one of the neutral Higgs bosons is demanded to have a mass around 126 GeV and SM-like properties, there can be substantially lighter Higgs bosons which have not been excluded yet by LEP or the 8 TeV run of the LHC. The decays of the heavier Higgs bosons or the SM-like resonance into a pair of light Higgs states which subsequently decay into other SM particles can lead to interesting signatures that can be investigated at the high-energy and high-luminosity run of the LHC. Furthermore, the discovery signatures of the very light and the heavy Higgs bosons directly decaying into SM final state particles will be analysed.