The global well-posedness of a new class of initial-boundary value problem on incompressible MHD-Boussinesq equations in the bounded domain with the smooth boundary is studied. Our models cover the incompressible NS equations, incompressible MHD equations and incompressible Boussinesq equations. The existence of global-in-time weak solution involved the integral terms at the boundary to the corresponding problem in two/three dimension is proven and the uniqueness of weak solution in the case of two dimension are obtained. The global existence and uniqueness of the strong and smooth solution to the corresponding problem in two-dimensional case for the smooth initial data is also proven.