In　this　paper,　we　discuss　with　the　global　well-posedness　of　2D　anisotropic　nonlinear　Boussinesq　equations　with　any　two　positive　viscosities　and　one　positive　thermal　diffusivity.　More　precisely,　for　three　kinds　of　viscous　combinations,　we　obtain　the　global　well-posedness　without　any　assumption　on　the　solution.　For　other　three　difficult　cases,　under　theminimal　regularity　assumption,　we　also　derive　the　unique　global　solution.　To　the　authors＇　knowledge,　our　result　is　new　even　for　the　simplified　model,　that　is,　F(theta)　=　theta　e(2).　Copyright　(C)　2017　John　Wiley　&　Sons,　Ltd.