Abstract: In a bounded domain of Ω⊂R² with smooth boundary, the homogeneous Neumann-Neumann-Dirichlet initial-boundary-value problem of a class of uncompressible Keller-Segel-Stokes equations system has been studied, and the global existence and boundedness of the classical solutions to this problem have been constructed under the appropriate smallness condition on the initial value of n₀. Thus what's next is to study the long-time behavior of the classical solutions based on the condition above, it is proven that the classical solutions to the problem converge to the spatial equilibrium at exponential rate as t goes to infinity under the extra smallness assumption on the initial data n₀, where thenn₀stands for the integral mean value of n over Ω, and the gravitational potential φ belongs to W^2,∞(Ω).