The　conditional　simulation　of　non-Gaussian　excitations　utilizing　records　from　the　monitoring　system　is　of　great　significance　for　hazard　mitigation.　To　this　end,　this　paper　proposes　a　novel　conditional　non-Gaussian　simulation　method.　In　this　method,　the　Unified　Hermite　Polynomial　Model　(UHPM)　is　used　to　describe　the　transformation　relationship　between　recorded　and　unrecorded　non-Gaussian　processes　and　their　underlying　Gaussian　counterparts.　Meanwhile,　an　explicit　transformation　model　between　their　correlation　functions　is　also　provided.　Then,　the　covariance　matrix　of　Fourier　coefficients　of　the　underlying　Gaussian　processes　is　constructed.　Based　on　this　covariance　matrix,　the　conditional　samples　of　Fourier　coefficients　are　generated　and　substituted　into　the　Spectral　Representation　Method　(SRM)　to　perform　the　conditional　simulation　of　the　underlying　Gaussian　processes.　Finally,　the　conditionally　simulated　samples　of　the　underlying　Gaussian　processes　are　transformed　into　the　nonGaussian　samples　by　the　UHPM.　To　showcase　the　precision　and　efficacy　of　the　proposed　method,　two　numerical　examples　involving　the　conditional　simulations　of　non-Gaussian　ground　motions　and　non-Gaussian　wind　pressure　coefficients　are　provided.