  This paper deals with stability and the large-time decay to any given global
smooth solutions of the 3D density-dependent incompressible Boussinesq system.
The decay rate for solutions of the corresponding Cauchy problem is obtained in
this work. With the aid of this decay rate, it is shown that a small
perturbation of initial data $(\overline{a}_0,\overline{\theta}_0,
\overline{u}_0)$ still generates a global smooth solution to the
density-dependent Boussinesq system, and this solution keeps close to the
reference solution.
