A　novel　speech　enhancement　method　with　Weighted　Denoising　Auto-encoder　(WDA)　is　proposed　in　this　paper.　A　weighted　reconstruction　loss　function　is　introduced　to　the　conventional　Denoising　Auto-encoder　(DA),　and　makes　it　suitable　for　the　task　of　speech　enhancement.　First,　the　proposed　WDA　is　used　to　model　the　relationship　between　the　noisy　and　clean　power　spectrums　of　speech　signal.　Then,　the　estimated　clean　power　spectrum　is　used　in　the　a　Posteriori　SNR　Controlled　Recursive　Averaging　(PCRA)　approach　for　the　estimation　of　the　a　priori　SNR.　Finally,　the　enhanced　speech　is　obtained　by　Wiener　filter　operating　in　the　frequency　domain.　From　the　test　results　under　ITU-T　G.160,　in　comparison　with　the　reference　method,　the　proposed　method　could　achieve　similar　amount　of　noise　reduction　in　both　white　and　colored　noise,　and　the　distortion　on　the　level　of　speech　signal　is　smaller.　Also,　the　objective　speech　quality　is　improved　in　all　the　test　conditions.