Reasonable　simulation　of　stochastic　fields　is　a　key　prerequisite　for　addressing　stochastic　mechanics　problems　with　Monte　Carlo　simulation　solver.　This　paper　presents　a　novel　method　to　simulate　m-variate　and　n-dimensional　(mV-nD)　homogenous　non-Gaussian　fields　according　to　the　prescribed　power　spectral　density　matrix　(PSDM)　and　first　four　moments.　In　the　proposed　method,　the　unified　Hermite　polynomial　model　(UHPM)　is　first　extended　to　mV-nD　homogenous　non-Gaussian　fields.　Then,　based　on　the　extended　UHPM,　a　complete　transformation　model　from　the　normalized　non-Gaussian　correlation　function　matrix　(CFM)　into　the　underlying　Gaussian　CFM　with　its　applicable　range　is　derived.　In　addition,　two　types　of　potential　incompatibility　of　the　transformation　arising　from　the　prescribed　PSDM　and　first　four　moments　are　defined　and　neatly　solved.　Finally,　a　unified　simulation　framework　for　mV-nD　homogenous　non-Gaussian　fields　is　presented,　where　the　fast　Fourier　transform　technique　can　be　embedded　in　both　spectral　representation　method　and　Wiener-Khintchine　transformation　to　speed　up　the　simulation　progress.　Two　numerical　examples　including　the　simulations　of　non-Gaussian　wind　fields　and　non-Gaussian　fields　of　material　properties　are　presented　to　demonstrate　the　effectiveness　of　the　proposed　method.