In　this　article,　we　studyweak　solutions　of　mean-field　stochastic　differential　equations　(SDEs),　also　known　as　McKean-Vlasov　equations,　whose　drift　b(s,　X-s,　Q(Xs)),　and　diffusion　coefficient　sigma　(s,　X-s,　Q(Xs))　depend　not　only　on　the　state　process　X-s　but　also　on　its　law.　We　suppose　that　b　and　sigma　are　bounded　and　continuous　in　the　state　as　well　as　the　probability　law;　the　continuity　with　respect　to　the　probability　law　is　understood　in　the　sense　of　the　2-Wasserstein　metric.　Using　the　approach　through　a　local　martingale　problem,　we　prove　the　existence　and　the　uniqueness　in　law　of　the　weak　solution　of　mean-field　SDEs.　The　uniqueness　in　law　is　obtained　if　the　associated　Cauchy　problem　possesses　for　all　initial　condition　f.　is　an　element　of　C-0(infinity)　(R-d)　a　classical　solution.　However,　unlike　the　classical　case,　the　Cauchy　problem　is　a　mean-field　PDE　as　recently　studied　by　Buckdahn　et　al.　[arXiv:1407.1215,　2014].　In　our　approach,　we　also　extend　the　Ito　formula　associated　with　mean-field　problems　given　by　Buckdahn　et　al.　to　a　more　general　case　of　coefficients.