In　this　paper,　we　propose　a　novel　loss　function　of　Non-Negative　Matrix　Factorization　(NMF)　based　on　focusing　energy　on　the　main　part.　Based　on　this　loss　function,　a　two-steps　model　and　a　new　Energy-Focused　Non-Negative　Matrix　Factorization　(EF-NMF)　model　are　derived　for　speech　enhancement.　We　use　the　statistical　distribution　to　explain　the　energy-focused　meaning　and　get　the　two　different　EF-NMF　models　inspired　by　the　greedy　algorithm.　Also,　IMCRA　is　combined　to　estimate　the　speech　energy　in　the　speech　energy-focused　elements.　Finally,　we　use　the　IMCRA　combined　with　EF-NMF　to　drive　linear　minimum　mean　square　error　(LMMSE)　estimator.　Comparing　with　the　classical　NMF　that　respectively　trains　the　noise　and　speech　basis　vectors,　the　EF-NMF　can　focus　more　speech　energy　on　the　speech　activation　matrix　when　it　decomposes　noisy　speech　signal.　The　experimental　results　show　that　the　EF-NMF　gives　better　quality　and　intelligibility　than　the　traditional　training　method　of　NMF,　and　better　speech　quality　is　gained　by　estimating　speech　elements　of　the　matrix　with　IMCRA.　©　2018　IEEE.