Recently,　deep　learning　techniques　have　significantly　promoted　the　development　of　speech　enhancement.　In　this　paper,　we　propose　a　novel　framework　to　conduct　speech　enhancement,　which　is　based　on　the　long　short-term　memory　networks　(LSTMs)　and　conditional　generative　adversarial　networks　(cGANs).　This　framework　includes　a　generator　(G)　and　a　discriminator　(D).　G　and　D　are　both　LSTMs　so　our　method　is　able　to　be　more　suitable　for　speech　enhancement　task　than　previous　deep　neural　network-based　methods.　In　this　study,　we　firstly　apply　this　framework　to　map　the　log-power　spectral　(LPS)　of　clean　speech　given　the　noisy　LPS　input.　In　addition,　this　framework　is　also　used　to　estimate　the　ideal　Wiener　filter　by　giving　the　noisy　Cepstral　input.　Experimental　results　indicate　that　our　strategy　can　not　only　improve　the　quality　and　intelligibility　of　noisy　speech,　but　also　is　competitive　to　other　deep　learning-based　approaches.